1
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Mi X, Michailidis AA, Shabani S, Miao KC, Klimov PV, Lloyd J, Rosenberg E, Acharya R, Aleiner I, Andersen TI, Ansmann M, Arute F, Arya K, Asfaw A, Atalaya J, Bardin JC, Bengtsson A, Bortoli G, Bourassa A, Bovaird J, Brill L, Broughton M, Buckley BB, Buell DA, Burger T, Burkett B, Bushnell N, Chen Z, Chiaro B, Chik D, Chou C, Cogan J, Collins R, Conner P, Courtney W, Crook AL, Curtin B, Dau AG, Debroy DM, Del Toro Barba A, Demura S, Di Paolo A, Drozdov IK, Dunsworth A, Erickson C, Faoro L, Farhi E, Fatemi R, Ferreira VS, Burgos LF, Forati E, Fowler AG, Foxen B, Genois É, Giang W, Gidney C, Gilboa D, Giustina M, Gosula R, Gross JA, Habegger S, Hamilton MC, Hansen M, Harrigan MP, Harrington SD, Heu P, Hoffmann MR, Hong S, Huang T, Huff A, Huggins WJ, Ioffe LB, Isakov SV, Iveland J, Jeffrey E, Jiang Z, Jones C, Juhas P, Kafri D, Kechedzhi K, Khattar T, Khezri M, Kieferová M, Kim S, Kitaev A, Klots AR, Korotkov AN, Kostritsa F, Kreikebaum JM, Landhuis D, Laptev P, Lau KM, Laws L, Lee J, Lee KW, Lensky YD, Lester BJ, Lill AT, Liu W, Locharla A, Malone FD, Martin O, McClean JR, McEwen M, Mieszala A, Montazeri S, Morvan A, Movassagh R, Mruczkiewicz W, Neeley M, Neill C, Nersisyan A, Newman M, Ng JH, Nguyen A, Nguyen M, Niu MY, O'Brien TE, Opremcak A, Petukhov A, Potter R, Pryadko LP, Quintana C, Rocque C, Rubin NC, Saei N, Sank D, Sankaragomathi K, Satzinger KJ, Schurkus HF, Schuster C, Shearn MJ, Shorter A, Shutty N, Shvarts V, Skruzny J, Smith WC, Somma R, Sterling G, Strain D, Szalay M, Torres A, Vidal G, Villalonga B, Heidweiller CV, White T, Woo BWK, Xing C, Yao ZJ, Yeh P, Yoo J, Young G, Zalcman A, Zhang Y, Zhu N, Zobrist N, Neven H, Babbush R, Bacon D, Boixo S, Hilton J, Lucero E, Megrant A, Kelly J, Chen Y, Roushan P, Smelyanskiy V, Abanin DA. Stable quantum-correlated many-body states through engineered dissipation. Science 2024; 383:1332-1337. [PMID: 38513021 DOI: 10.1126/science.adh9932] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Accepted: 02/13/2024] [Indexed: 03/23/2024]
Abstract
Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.
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Affiliation(s)
- X Mi
- Google Research, Mountain View, CA, USA
| | - A A Michailidis
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
| | - S Shabani
- Google Research, Mountain View, CA, USA
| | - K C Miao
- Google Research, Mountain View, CA, USA
| | | | - J Lloyd
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
| | | | - R Acharya
- Google Research, Mountain View, CA, USA
| | - I Aleiner
- Google Research, Mountain View, CA, USA
| | | | - M Ansmann
- Google Research, Mountain View, CA, USA
| | - F Arute
- Google Research, Mountain View, CA, USA
| | - K Arya
- Google Research, Mountain View, CA, USA
| | - A Asfaw
- Google Research, Mountain View, CA, USA
| | - J Atalaya
- Google Research, Mountain View, CA, USA
| | - J C Bardin
- Google Research, Mountain View, CA, USA
- Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA
| | | | - G Bortoli
- Google Research, Mountain View, CA, USA
| | | | - J Bovaird
- Google Research, Mountain View, CA, USA
| | - L Brill
- Google Research, Mountain View, CA, USA
| | | | | | - D A Buell
- Google Research, Mountain View, CA, USA
| | - T Burger
- Google Research, Mountain View, CA, USA
| | - B Burkett
- Google Research, Mountain View, CA, USA
| | | | - Z Chen
- Google Research, Mountain View, CA, USA
| | - B Chiaro
- Google Research, Mountain View, CA, USA
| | - D Chik
- Google Research, Mountain View, CA, USA
| | - C Chou
- Google Research, Mountain View, CA, USA
| | - J Cogan
- Google Research, Mountain View, CA, USA
| | - R Collins
- Google Research, Mountain View, CA, USA
| | - P Conner
- Google Research, Mountain View, CA, USA
| | | | - A L Crook
- Google Research, Mountain View, CA, USA
| | - B Curtin
- Google Research, Mountain View, CA, USA
| | - A G Dau
- Google Research, Mountain View, CA, USA
| | | | | | - S Demura
- Google Research, Mountain View, CA, USA
| | | | | | | | | | - L Faoro
- Google Research, Mountain View, CA, USA
| | - E Farhi
- Google Research, Mountain View, CA, USA
| | - R Fatemi
- Google Research, Mountain View, CA, USA
| | | | | | - E Forati
- Google Research, Mountain View, CA, USA
| | | | - B Foxen
- Google Research, Mountain View, CA, USA
| | - É Genois
- Google Research, Mountain View, CA, USA
| | - W Giang
- Google Research, Mountain View, CA, USA
| | - C Gidney
- Google Research, Mountain View, CA, USA
| | - D Gilboa
- Google Research, Mountain View, CA, USA
| | | | - R Gosula
- Google Research, Mountain View, CA, USA
| | - J A Gross
- Google Research, Mountain View, CA, USA
| | | | - M C Hamilton
- Google Research, Mountain View, CA, USA
- Department of Electrical and Computer Engineering, Auburn University, Auburn, AL, USA
| | - M Hansen
- Google Research, Mountain View, CA, USA
| | | | | | - P Heu
- Google Research, Mountain View, CA, USA
| | | | - S Hong
- Google Research, Mountain View, CA, USA
| | - T Huang
- Google Research, Mountain View, CA, USA
| | - A Huff
- Google Research, Mountain View, CA, USA
| | | | - L B Ioffe
- Google Research, Mountain View, CA, USA
| | | | - J Iveland
- Google Research, Mountain View, CA, USA
| | - E Jeffrey
- Google Research, Mountain View, CA, USA
| | - Z Jiang
- Google Research, Mountain View, CA, USA
| | - C Jones
- Google Research, Mountain View, CA, USA
| | - P Juhas
- Google Research, Mountain View, CA, USA
| | - D Kafri
- Google Research, Mountain View, CA, USA
| | | | - T Khattar
- Google Research, Mountain View, CA, USA
| | - M Khezri
- Google Research, Mountain View, CA, USA
| | - M Kieferová
- Google Research, Mountain View, CA, USA
- Centre for Quantum Software and Information (QSI), Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW, Australia
| | - S Kim
- Google Research, Mountain View, CA, USA
| | - A Kitaev
- Google Research, Mountain View, CA, USA
| | - A R Klots
- Google Research, Mountain View, CA, USA
| | - A N Korotkov
- Google Research, Mountain View, CA, USA
- Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA
| | | | | | | | - P Laptev
- Google Research, Mountain View, CA, USA
| | - K-M Lau
- Google Research, Mountain View, CA, USA
| | - L Laws
- Google Research, Mountain View, CA, USA
| | - J Lee
- Google Research, Mountain View, CA, USA
- Department of Chemistry, Columbia University, New York, NY, USA
| | - K W Lee
- Google Research, Mountain View, CA, USA
| | | | | | - A T Lill
- Google Research, Mountain View, CA, USA
| | - W Liu
- Google Research, Mountain View, CA, USA
| | | | | | - O Martin
- Google Research, Mountain View, CA, USA
| | | | - M McEwen
- Google Research, Mountain View, CA, USA
| | | | | | - A Morvan
- Google Research, Mountain View, CA, USA
| | | | | | - M Neeley
- Google Research, Mountain View, CA, USA
| | - C Neill
- Google Research, Mountain View, CA, USA
| | | | - M Newman
- Google Research, Mountain View, CA, USA
| | - J H Ng
- Google Research, Mountain View, CA, USA
| | - A Nguyen
- Google Research, Mountain View, CA, USA
| | - M Nguyen
- Google Research, Mountain View, CA, USA
| | - M Y Niu
- Google Research, Mountain View, CA, USA
| | | | | | | | - R Potter
- Google Research, Mountain View, CA, USA
| | - L P Pryadko
- Google Research, Mountain View, CA, USA
- Department of Physics and Astronomy, University of California, Riverside, CA, USA
| | | | - C Rocque
- Google Research, Mountain View, CA, USA
| | - N C Rubin
- Google Research, Mountain View, CA, USA
| | - N Saei
- Google Research, Mountain View, CA, USA
| | - D Sank
- Google Research, Mountain View, CA, USA
| | | | | | | | | | | | - A Shorter
- Google Research, Mountain View, CA, USA
| | - N Shutty
- Google Research, Mountain View, CA, USA
| | - V Shvarts
- Google Research, Mountain View, CA, USA
| | - J Skruzny
- Google Research, Mountain View, CA, USA
| | - W C Smith
- Google Research, Mountain View, CA, USA
| | - R Somma
- Google Research, Mountain View, CA, USA
| | | | - D Strain
- Google Research, Mountain View, CA, USA
| | - M Szalay
- Google Research, Mountain View, CA, USA
| | - A Torres
- Google Research, Mountain View, CA, USA
| | - G Vidal
- Google Research, Mountain View, CA, USA
| | | | | | - T White
- Google Research, Mountain View, CA, USA
| | - B W K Woo
- Google Research, Mountain View, CA, USA
| | - C Xing
- Google Research, Mountain View, CA, USA
| | - Z J Yao
- Google Research, Mountain View, CA, USA
| | - P Yeh
- Google Research, Mountain View, CA, USA
| | - J Yoo
- Google Research, Mountain View, CA, USA
| | - G Young
- Google Research, Mountain View, CA, USA
| | - A Zalcman
- Google Research, Mountain View, CA, USA
| | - Y Zhang
- Google Research, Mountain View, CA, USA
| | - N Zhu
- Google Research, Mountain View, CA, USA
| | - N Zobrist
- Google Research, Mountain View, CA, USA
| | - H Neven
- Google Research, Mountain View, CA, USA
| | - R Babbush
- Google Research, Mountain View, CA, USA
| | - D Bacon
- Google Research, Mountain View, CA, USA
| | - S Boixo
- Google Research, Mountain View, CA, USA
| | - J Hilton
- Google Research, Mountain View, CA, USA
| | - E Lucero
- Google Research, Mountain View, CA, USA
| | - A Megrant
- Google Research, Mountain View, CA, USA
| | - J Kelly
- Google Research, Mountain View, CA, USA
| | - Y Chen
- Google Research, Mountain View, CA, USA
| | - P Roushan
- Google Research, Mountain View, CA, USA
| | | | - D A Abanin
- Google Research, Mountain View, CA, USA
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
- Department of Physics, Princeton University, Princeton, NJ, USA
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2
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Schmidt HJ, Gemmer J. Stochastic Thermodynamics of a Finite Quantum System Coupled to Two Heat Baths. ENTROPY (BASEL, SWITZERLAND) 2023; 25:504. [PMID: 36981392 PMCID: PMC10048248 DOI: 10.3390/e25030504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Revised: 03/10/2023] [Accepted: 03/13/2023] [Indexed: 06/18/2023]
Abstract
We consider a situation where an N-level system (NLS) is coupled successively to two heat baths with different temperatures without being necessarily thermalized and approaches a steady state. For this situation we apply a general Jarzynski-type equation and conclude that heat and entropy is flowing from the hot bath to the cold one. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities. Our approach is illustrated by an analytical example. For the linear regime, i.e., for small temperature differences between the two heat baths, we derive an expression for the heat conduction coefficient.
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3
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de Paula AL, Pereira E. Establishing non-zero energy currents with the one-way street phenomenon and other symmetry properties in boundary driven spin systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:445601. [PMID: 35995040 DOI: 10.1088/1361-648x/ac8bbe] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2022] [Accepted: 08/22/2022] [Indexed: 06/15/2023]
Abstract
The aim of this paper is the investigation of properties of the energy current of usual (frequently found in the literature) boundary driven spin systems. For inhomogeneous Heisenberg (XXZandXXX) spin chains, we numerically compute the steady state, in the absence of an external magnetic field, and confirm the previously shown occurrence of the one-way street phenomenon, precisely, there is a nonzero energy current that preserves its magnitude and direction as we invert the baths at the edges, an effect stronger than the perfect rectification (which means current in a direction and zero current as we invert the baths). The consideration of several different polarizations at the edges reestablishes that it is a ubiquitous phenomenon. And, even for these inhomogeneous versions of spin chains, we also establish, by analytical methods, other symmetry properties of the energy current and confirm them by numerical computations.
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Affiliation(s)
- Alberto L de Paula
- Instituto Federal de Educação, Ciência e Tecnologia de Minas Gerais, C. P. 169, Ribeirão das Neves 33858-480, MG, Brazil
| | - Emmanuel Pereira
- Departamento de Física, Universidade Federal de Minas Gerais, C. P. 702, Belo Horizonte 30123-970, MG, Brazil
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4
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Akemann G, Mielke A, Päßler P. Spacing distribution in the two-dimensional Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at noninteger β. Phys Rev E 2022; 106:014146. [PMID: 35974587 DOI: 10.1103/physreve.106.014146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 07/07/2022] [Indexed: 06/15/2023]
Abstract
A random matrix representation is proposed for the two-dimensional (2D) Coulomb gas at inverse temperature β. For 2×2 matrices with Gaussian distribution we analytically compute the nearest-neighbor spacing distribution of complex eigenvalues in radial distance. Because it does not provide such a good approximation as the Wigner surmise in 1D, we introduce an effective β_{eff}(β) in our analytic formula that describes the spacing obtained numerically from the 2D Coulomb gas well for small values of β. It reproduces the 2D Poisson distribution at β=0 exactly, that is valid for a large particle number. The surmise is used to fit data in two examples, from open quantum spin chains and ecology. The spacing distributions of complex symmetric and complex quaternion self-dual ensembles of non-Hermitian random matrices, that are only known numerically, are very well fitted by noninteger values β=1.4 and β=2.6 from a 2D Coulomb gas, respectively. These two ensembles have been suggested as the only two symmetry classes, where the 2D bulk statistics is different from the Ginibre ensemble.
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Affiliation(s)
- Gernot Akemann
- Faculty of Physics, Bielefeld University, Postfach 100131, 33501 Bielefeld, Germany
| | - Adam Mielke
- Technical University of Denmark, Asmussens Allé, Building 303B, 2800 Kgs. Lyngby, Denmark
| | - Patricia Päßler
- Faculty of Physics, Bielefeld University, Postfach 100131, 33501 Bielefeld, Germany
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5
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Lee KH, Balachandran V, Guo C, Poletti D. Transport and spectral properties of the XX+XXZ diode and stability to dephasing. Phys Rev E 2022; 105:024120. [PMID: 35291148 DOI: 10.1103/physreve.105.024120] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Accepted: 01/26/2022] [Indexed: 06/14/2023]
Abstract
We study the transport and spectral property of a segmented diode formed by an XX+XXZ spin chain. This system has been shown to become an ideal rectifier for spin current for large enough anisotropy. Here we show numerical evidence that the system in reverse bias has signatures pointing toward the existence of three different transport regimes depending on the value of the anisotropy: ballistic, diffusive, and insulating. In forward bias we observe two regimes, ballistic and diffusive. The system in forward and reverse bias shows significantly different spectral properties, with distribution of rapidities converging toward different functions. In the presence of dephasing the system becomes diffusive, rectification is significantly reduced, the relaxation gap increases, and the spectral properties in forward and reverse bias tend to converge. For large dephasing the relaxation gap decreases again as a result of quantum Zeno physics.
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Affiliation(s)
- Kang Hao Lee
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - Vinitha Balachandran
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - Chu Guo
- Henan Key Laboratory of Quantum Information and Cryptography, Zhengzhou, Henan 450000, China
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
| | - Dario Poletti
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
- Engineering Product Development Pillar, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
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6
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de Leeuw M, Paletta C, Pozsgay B. Constructing Integrable Lindblad Superoperators. PHYSICAL REVIEW LETTERS 2021; 126:240403. [PMID: 34213919 DOI: 10.1103/physrevlett.126.240403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 05/20/2021] [Indexed: 06/13/2023]
Abstract
We develop a new method for the construction of one-dimensional integrable Lindblad systems, which describe quantum many body models in contact with a Markovian environment. We find several new models with interesting features, such as annihilation-diffusion processes, a mixture of coherent and classical particle propagation, and a rectified steady state current. We also find new ways to represent known classical integrable stochastic equations by integrable Lindblad operators. Our method can be extended to various other situations and it establishes a structured approach to the study of solvable open quantum systems.
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Affiliation(s)
- Marius de Leeuw
- School of Mathematics & Hamilton Mathematics Institute, Trinity College Dublin, Dublin, Ireland
| | - Chiara Paletta
- School of Mathematics & Hamilton Mathematics Institute, Trinity College Dublin, Dublin, Ireland
| | - Balázs Pozsgay
- Department of Theoretical Physics & MTA-ELTE "Momentum" Integrable Quantum Dynamics Research Group, Eötvös Loránd University, Budapest, Hungary
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7
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Popkov V, Presilla C. Full Spectrum of the Liouvillian of Open Dissipative Quantum Systems in the Zeno Limit. PHYSICAL REVIEW LETTERS 2021; 126:190402. [PMID: 34047584 DOI: 10.1103/physrevlett.126.190402] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2021] [Accepted: 04/12/2021] [Indexed: 06/12/2023]
Abstract
We consider an open quantum system with dissipation, described by a Lindblad Master equation (LME). For dissipation locally acting and sufficiently strong, a separation of the relaxation timescales occurs, which, in terms of the eigenvalues of the Liouvillian, implies a grouping of the latter in distinct vertical stripes in the complex plane at positions determined by the eigenvalues of the dissipator. We derive effective LME equations describing the modes within each stripe separately, and solve them perturbatively, obtaining for the full set of eigenvalues and eigenstates of the Liouvillian explicit expressions correct at order 1/Γ included, where Γ is the strength of the dissipation. As an example, we apply our general results to quantum XYZ spin chains coupled, at one boundary, to a dissipative bath of polarization.
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Affiliation(s)
- Vladislav Popkov
- Department of Physics, University of Wuppertal, Gaussstraße 20, 42119 Wuppertal, Germany
| | - Carlo Presilla
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, Roma 00185, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Roma 00185, Italy
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8
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Nakagawa M, Kawakami N, Ueda M. Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model. PHYSICAL REVIEW LETTERS 2021; 126:110404. [PMID: 33798340 DOI: 10.1103/physrevlett.126.110404] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Accepted: 02/12/2021] [Indexed: 06/12/2023]
Abstract
A one-dimensional dissipative Hubbard model with two-body loss is shown to be exactly solvable. We obtain an exact eigenspectrum of a Liouvillian superoperator by employing a non-Hermitian extension of the Bethe-ansatz method. We find steady states, the Liouvillian gap, and an exceptional point that is accompanied by the divergence of the correlation length. A dissipative version of spin-charge separation induced by the quantum Zeno effect is also demonstrated. Our result presents a new class of exactly solvable Liouvillians of open quantum many-body systems, which can be tested with ultracold atoms subject to inelastic collisions.
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Affiliation(s)
- Masaya Nakagawa
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Norio Kawakami
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Masahito Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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9
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Poulsen K, Zinner NT. Giant Magnetoresistance in Boundary-Driven Spin Chains. PHYSICAL REVIEW LETTERS 2021; 126:077203. [PMID: 33666455 DOI: 10.1103/physrevlett.126.077203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2020] [Accepted: 01/08/2021] [Indexed: 06/12/2023]
Abstract
In solid state physics, giant magnetoresistance is the large change in electrical resistance due to an external magnetic field. Here we show that giant magnetoresistance is possible in a spin chain composed of weakly interacting layers of strongly coupled spins. This is found for all system sizes even down to a minimal system of four spins. The mechanism driving the effect is a mismatch in the energy spectrum resulting in spin excitations being reflected at the boundaries between layers. This mismatch, and thus the current, can be controlled by external magnetic fields resulting in giant magnetoresistance. A simple rule for determining the behavior of the spin transport under the influence of a magnetic field is presented based on the energy levels of the strongly coupled spins.
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Affiliation(s)
- Kasper Poulsen
- Department of Physics and Astronomy, Aarhus University, Ny munkegade 120, 8000 Aarhus C, Denmark
| | - Nikolaj T Zinner
- Department of Physics and Astronomy, Aarhus University, Ny munkegade 120, 8000 Aarhus C, Denmark and Aarhus Institute of Advanced Studies, Aarhus University, Høegh-Guldbergs Gade 6B, 8000 Aarhus C, Denmark
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10
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Perfetto G, Gambassi A. Dynamics of large deviations in the hydrodynamic limit: Noninteracting systems. Phys Rev E 2020; 102:042128. [PMID: 33212614 DOI: 10.1103/physreve.102.042128] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2020] [Accepted: 09/29/2020] [Indexed: 11/07/2022]
Abstract
We study the dynamics of the statistics of the energy transferred across a point along a quantum chain which is prepared in the inhomogeneous initial state obtained by joining two identical semi-infinite parts thermalized at two different temperatures. In particular, we consider the transverse field Ising and harmonic chains as prototypical models of noninteracting fermionic and bosonic excitations, respectively. Within the so-called hydrodynamic limit of large space-time scales we first discuss the mean values of the energy density and current, and then, aiming at the statistics of fluctuations, we calculate exactly the scaled cumulant generating function of the transferred energy. From the latter, the evolution of the associated large deviation function is obtained. A natural interpretation of our results is provided in terms of a semiclassical picture of quasiparticles moving ballistically along classical trajectories. Similarities and differences between the transferred energy scaled cumulant and the large deviation functions in the cases of noninteracting fermions and bosons are discussed.
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Affiliation(s)
- Gabriele Perfetto
- SISSA-International School for Advanced Studies, via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di Trieste, via Bonomea 265, 34136, Trieste, Italy
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies, via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di Trieste, via Bonomea 265, 34136, Trieste, Italy
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11
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Lee KH, Balachandran V, Tan R, Guo C, Poletti D. Giant Spin Current Rectification Due to the Interplay of Negative Differential Conductance and a Non-Uniform Magnetic Field. ENTROPY 2020; 22:e22111311. [PMID: 33287076 PMCID: PMC7711849 DOI: 10.3390/e22111311] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/08/2020] [Revised: 11/06/2020] [Accepted: 11/15/2020] [Indexed: 11/16/2022]
Abstract
In XXZ chains with large enough interactions, spin transport can be significantly suppressed when the bias of the dissipative driving becomes large enough. This phenomenon of negative differential conductance is caused by the formation of two oppositely polarized ferromagnetic domains at the edges of the chain. Here, we show that this many-body effect, combined with a non-uniform magnetic field, can allow for a high degree of control of the spin current. In particular, by studying all of the possible shapes of local magnetic fields potentials, we find that a configuration in which the magnetic field points up for half of the chain and down for the other half, can result in giant spin-current rectification, for example, up to 108 for a system with only 8 spins. Our results show clear indications that the rectification can increase with the system size.
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Affiliation(s)
- Kang Hao Lee
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore;
| | - Vinitha Balachandran
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore;
- Correspondence: (V.B.); (D.P.)
| | - Ryan Tan
- Engineering Product Development Pillar, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore;
| | - Chu Guo
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China;
| | - Dario Poletti
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore;
- Engineering Product Development Pillar, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore;
- Correspondence: (V.B.); (D.P.)
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12
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Finsterhölzl R, Katzer M, Knorr A, Carmele A. Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E984. [PMID: 33286753 PMCID: PMC7597300 DOI: 10.3390/e22090984] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Revised: 08/28/2020] [Accepted: 09/01/2020] [Indexed: 11/20/2022]
Abstract
This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.
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Affiliation(s)
- Regina Finsterhölzl
- Institut für Theoretische Physik, Nichtlineare Optik und Quantenelektronik, Hardenbergstraße 36, 10623 Berlin, Germany; (M.K.); (A.K.); (A.C.)
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13
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Carollo F, Pérez-Espigares C. Entanglement statistics in Markovian open quantum systems: A matter of mutation and selection. Phys Rev E 2020; 102:030104. [PMID: 33076006 DOI: 10.1103/physreve.102.030104] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2019] [Accepted: 09/09/2020] [Indexed: 06/11/2023]
Abstract
Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behavior and for its possible application in near-term quantum technologies. However, understanding these fluctuations is extremely challenging due, to a large extent, to a lack of efficient important sampling methods for quantum systems. Here, we devise a unified framework-based on population-dynamics methods-for the evaluation of the full probability distribution of generic time-integrated observables in Markovian quantum jump processes. These include quantities carrying information about genuine quantum features, such as quantum superposition or entanglement, not accessible with existing numerical techniques. The algorithm we propose provides dynamical free-energy and entropy functionals which, akin to their equilibrium counterpart, permit one to unveil intriguing phase-transition behavior in quantum trajectories. We discuss some applications and further disclose coexistence and hysteresis, between a highly entangled phase and a low entangled one, in large fluctuations of a strongly interacting few-body system.
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Affiliation(s)
- Federico Carollo
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Carlos Pérez-Espigares
- Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada 18071, Spain
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14
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Reslen J. Uncoupled Majorana fermions in open quantum systems: on the efficient simulation of non-equilibrium stationary states of quadratic Fermi models. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:405601. [PMID: 32396886 DOI: 10.1088/1361-648x/ab926d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2020] [Accepted: 05/12/2020] [Indexed: 06/11/2023]
Abstract
A decomposition of the non-equilibrium stationary state of a quadratic Fermi system influenced by linear baths is obtained and used to establish a simulation protocol in terms of tensor states. The scheme is then applied to examine the occurrence of uncoupled Majorana fermions in Kitaev chains subject to baths on the ends. The resulting phase diagram is compared against the topological characterization of the equilibrium chain and the protocol efficiency is studied with respect to this model.
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Affiliation(s)
- Jose Reslen
- Coordinación de Física, Universidad del Atlántico, Kilómetro 7 Antigua vía a Puerto Colombia, A.A. 1890, Barranquilla, Colombia
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15
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Shirai T, Mori T. Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys Rev E 2020; 101:042116. [PMID: 32422755 DOI: 10.1103/physreve.101.042116] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2019] [Accepted: 03/20/2020] [Indexed: 11/07/2022]
Abstract
We investigate steady states of macroscopic quantum systems under dissipation not obeying the detailed balance condition. We argue that the Gibbs state at an effective temperature gives a good description of the steady state provided that the system Hamiltonian obeys the eigenstate thermalization hypothesis (ETH) and the perturbation theory in the weak system-environment coupling is valid in the thermodynamic limit. We derive a criterion to guarantee the validity of the perturbation theory, which is satisfied in the thermodynamic limit for sufficiently weak dissipation when the Liouvillian is gapped for bulk-dissipated systems, while the perturbation theory breaks down in boundary-dissipated chaotic systems due to the presence of diffusive transports. We numerically confirm these theoretical predictions. This paper suggests a connection between steady states of macroscopic open quantum systems and the ETH.
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Affiliation(s)
- Tatsuhiko Shirai
- Green Computing Systems Research Organization, Waseda University, Tokyo 162-0042, Japan
| | - Takashi Mori
- RIKEN Center for Emergent Matter Science, Wako 351-0198, Japan
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16
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Aurell E, Donvil B, Mallick K. Large deviations and fluctuation theorem for the quantum heat current in the spin-boson model. Phys Rev E 2020; 101:052116. [PMID: 32575222 DOI: 10.1103/physreve.101.052116] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Accepted: 03/16/2020] [Indexed: 11/07/2022]
Abstract
We study the heat current flowing between two baths consisting of harmonic oscillators interacting with a qubit through a spin-boson coupling. An explicit expression for the generating function of the total heat flowing between the right and left baths is derived by evaluating the corresponding Feynman-Vernon path integral by performing the noninteracting blip approximation (NIBA). We recover the known expression, obtained by using the polaron transform. This generating function satisfies the Gallavotti-Cohen fluctuation theorem, both before and after performing the NIBA. We also verify that the heat conductance is proportional to the variance of the heat current, retrieving the well-known fluctuation dissipation relation. Finally, we present numerical results for the heat current.
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Affiliation(s)
- Erik Aurell
- KTH Royal Institute of Technology, AlbaNova University Center, SE-106 91 Stockholm, Sweden and Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kraków, Poland
| | - Brecht Donvil
- Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland
| | - Kirone Mallick
- Institut de Physique Théorique, Université Paris-Saclay, CEA and CNRS, 91191 Gif-sur-Yvette, France
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17
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Wurtz J, Polkovnikov A. Quantum diffusion in spin chains with phase space methods. Phys Rev E 2020; 101:052120. [PMID: 32575223 DOI: 10.1103/physreve.101.052120] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2018] [Accepted: 04/17/2020] [Indexed: 06/11/2023]
Abstract
Connecting short-time microscopic dynamics with long-time hydrodynamics in strongly correlated quantum systems is one of the outstanding questions. In particular, it is hard to determine various hydrodynamic coefficients such as the diffusion constant or viscosity starting from a microscopic model: exact quantum simulations are limited to either small system sizes or to short times, which are insufficient to reach asymptotic behavior and so various approximations must be applied. We show that these difficulties, at least for particular models, can be circumvented by using the cluster truncated Wigner approximation (CTWA), which maps quantum Hamiltonian dynamics into classical Hamiltonian dynamics in auxiliary high-dimensional phase space. We apply CTWA to XXZ next-nearest-neighbor spin-1/2 chains and XY spin ladders, and find behavior consisting of short-time spin relaxation which gradually crosses over to emergent diffusive behavior at long times. For a random initial state, we show that CTWA correctly reproduces the whole spin spectral function. Necessary in this construction is sampling from properly fluctuating initial conditions: the Dirac mean-field (variational) ansatz, which neglects such fluctuations, leads to incorrect predictions.
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Affiliation(s)
- Jonathan Wurtz
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Anatoli Polkovnikov
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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18
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19
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Popkov V, Prosen T, Zadnik L. Exact Nonequilibrium Steady State of Open XXZ/XYZ Spin-1/2 Chain with Dirichlet Boundary Conditions. PHYSICAL REVIEW LETTERS 2020; 124:160403. [PMID: 32383905 DOI: 10.1103/physrevlett.124.160403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2019] [Accepted: 03/23/2020] [Indexed: 06/11/2023]
Abstract
We investigate a dissipatively driven XYZ spin-1/2 chain in the Zeno limit of strong dissipation, described by the Lindblad master equation. The nonequilibrium steady state is expressed in terms of a matrix product ansatz using novel site-dependent Lax operators. The components of Lax operators satisfy a simple set of linear recurrence equations that generalize the defining algebraic relations of the quantum group U_{q}(sl_{2}). We reveal connection between the nonequilibrium steady state of the nonunitary dynamics and the respective integrable model with edge magnetic fields, described by coherent unitary dynamics.
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Affiliation(s)
- Vladislav Popkov
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
- Bergische Universität Wuppertal, Gauss-Strasse 20, D-42097 Wuppertal, Germany
| | - Tomaž Prosen
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
| | - Lenart Zadnik
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
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20
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de Paula AL, Pereira E, Drumond RC, Aguiar MCO. Energy current manipulation and reversal of rectification in graded XXZ spin chains. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:175403. [PMID: 31935711 DOI: 10.1088/1361-648x/ab6b8c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This work is devoted to the investigation of nontrivial transport properties in many-body quantum systems. Precisely, we study transport in the steady state of spin-1/2 Heisenberg XXZ chains, driven out of equilibrium by two magnetic baths at their end points. We take graded versions of the model, i.e. asymmetric chains in which some structure gradually changes in space. We investigate how we can manipulate and control the energy and spin currents of such chains by tuning external and/or inner parameters. In particular, we describe the occurrence of energy current rectification and its reversal due to the application of external magnetic fields. We show that, after carefully chosen inner parameters for the system, by turning on an external magnetic field we can find spin and energy currents propagating in different directions. More interestingly, we may find cases in which rectifications of energy and spin currents occur in opposite directions, i.e. if the energy current is larger when flowing from left to right side, then the spin current is larger if it flows from right to left side. We still describe situations with inversion of the energy current direction as we increase the system asymmetry. We stress that our work aims the development of theoretical knowledge as well as the stimulation of future experimental applications.
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Affiliation(s)
- Alberto L de Paula
- Departamento de Física, Universidade Federal de Minas Gerais, C. P. 702, 30123-970, Belo Horizonte, MG, Brazil. Instituto Federal de Educação, Ciência e Tecnologia do Rio de Janeiro, C. P. 121, 20270-021, Rio de Janeiro, RJ, Brazil
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21
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Popkov V, Prosen T, Zadnik L. Inhomogeneous matrix product ansatz and exact steady states of boundary-driven spin chains at large dissipation. Phys Rev E 2020; 101:042122. [PMID: 32422721 DOI: 10.1103/physreve.101.042122] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Accepted: 03/23/2020] [Indexed: 06/11/2023]
Abstract
We find novel site-dependent Lax operators in terms of which we demonstrate exact solvability of a dissipatively driven XYZ spin-1/2 chain in the Zeno limit of strong dissipation, with jump operators polarizing the boundary spins in arbitrary directions. We write the corresponding nonequilibrium steady state using an inhomogeneous matrix product ansatz, where the constituent matrices satisfy a simple set of linear recurrence relations. Although these matrices can be embedded into an infinite-dimensional auxiliary space, we have verified that they cannot be simultaneously put into a tridiagonal form, not even in the case of axially symmetric (XXZ) bulk interactions and general nonlongitudinal boundary dissipation. We expect our results to have further fundamental applications for the construction of nonlocal integrals of motion for the open XYZ model with arbitrary boundary fields, or the eight-vertex model.
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Affiliation(s)
- Vladislav Popkov
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
- Bergische Universität Wuppertal, Gauss-Strasse 20, D-42097 Wuppertal, Germany
| | - Tomaž Prosen
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
| | - Lenart Zadnik
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
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22
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Mierzejewski M, Vidmar L. Quantitative Impact of Integrals of Motion on the Eigenstate Thermalization Hypothesis. PHYSICAL REVIEW LETTERS 2020; 124:040603. [PMID: 32058771 DOI: 10.1103/physrevlett.124.040603] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2019] [Revised: 11/26/2019] [Indexed: 06/10/2023]
Abstract
Even though the eigenstate thermalization hypothesis (ETH) may be introduced as an extension of the random matrix theory, physical Hamiltonians and observables differ from random operators. One of the challenges is to embed local integrals of motion (LIOMs) within the ETH. Here we make steps towards a unified treatment of the ETH in integrable and nonintegrable models with translational invariance. Specifically, we focus on the impact of LIOMs on the fluctuations and structure of the diagonal matrix elements of local observables. We first show that nonvanishing fluctuations entail the presence of LIOMs. Then we introduce a generic protocol to construct observables, subtracted by their projections on LIOMs as well as products of LIOMs. The protocol systematically reduces fluctuations and/or the structure of the diagonal matrix elements. We verify our arguments by numerical results for integrable and nonintegrable models.
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Affiliation(s)
- Marcin Mierzejewski
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - Lev Vidmar
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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23
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Akemann G, Kieburg M, Mielke A, Prosen T. Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems. PHYSICAL REVIEW LETTERS 2019; 123:254101. [PMID: 31922808 DOI: 10.1103/physrevlett.123.254101] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2019] [Indexed: 06/10/2023]
Abstract
We study the transition between integrable and chaotic behavior in dissipative open quantum systems, exemplified by a boundary driven quantum spin chain. The repulsion between the complex eigenvalues of the corresponding Liouville operator in radial distance s is used as a universal measure. The corresponding level spacing distribution is well fitted by that of a static two-dimensional Coulomb gas with harmonic potential at inverse temperature β∈[0,2]. Here, β=0 yields the two-dimensional Poisson distribution, matching the integrable limit of the system, and β=2 equals the distribution obtained from the complex Ginibre ensemble, describing the fully chaotic limit. Our findings generalize the results of Grobe, Haake, and Sommers, who derived a universal cubic level repulsion for small spacings s. We collect mathematical evidence for the universality of the full level spacing distribution in the fully chaotic limit at β=2. It holds for all three Ginibre ensembles of random matrices with independent real, complex, or quaternion matrix elements.
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Affiliation(s)
- Gernot Akemann
- Faculty of Physics, Bielefeld University, Postfach 100131, 33501 Bielefeld, Germany and Department of Mathematics, Royal Institute of Technology (KTH), Brinellvägen 8, 114 28 Stockholm, Sweden
| | - Mario Kieburg
- School of Mathematics and Statistics, University of Melbourne, 813 Swanston Street, Parkville, Melbourne, Victoria 3010, Australia
| | - Adam Mielke
- Faculty of Physics, Bielefeld University, Postfach 100131, 33501 Bielefeld, Germany
| | - Tomaž Prosen
- Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana 1000, Slovenia
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24
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Carollo F, Gillman E, Weimer H, Lesanovsky I. Critical Behavior of the Quantum Contact Process in One Dimension. PHYSICAL REVIEW LETTERS 2019; 123:100604. [PMID: 31573316 DOI: 10.1103/physrevlett.123.100604] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Indexed: 06/10/2023]
Abstract
The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a nonequilibrium phase transition into an absorbing state that has been widely investigated and shown to belong to the directed percolation universality class. When the same process is considered in a quantum setting, much less is known. So far, mainly semiclassical studies have been conducted and the nature of the transition in low dimensions is still a matter of debate. Also, from a numerical point of view, from which the system may look fairly simple-especially in one dimension-results are lacking. In particular, the presence of the absorbing state poses a substantial challenge, which appears to affect the reliability of algorithms targeting directly the steady state. Here we perform real-time numerical simulations of the open dynamics of the quantum contact process and shed light on the existence and on the nature of an absorbing state phase transition in one dimension. We find evidence for the transition being continuous and provide first estimates for the critical exponents. Beyond the conceptual interest, the simplicity of the quantum contact process makes it an ideal benchmark problem for scrutinizing numerical methods for open quantum nonequilibrium systems.
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Affiliation(s)
- Federico Carollo
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Edward Gillman
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Hendrik Weimer
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
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25
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Palmero M, Xu X, Guo C, Poletti D. Thermalization with detailed-balanced two-site Lindblad dissipators. Phys Rev E 2019; 100:022111. [PMID: 31574662 DOI: 10.1103/physreve.100.022111] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Indexed: 06/10/2023]
Abstract
The use of two-site Lindblad dissipators to generate thermal states and study heat transport was raised to prominence by Prosen and Žnidarič [J. Stat. Mech. (2009) P020351742-546810.1088/1742-5468/2009/02/P02035]. Here we propose a variant of this method based on detailed balance of internal levels of the two-site Hamiltonian and characterize its performance. We study the thermalization profile in the chain, the effective temperatures achieved by different single- and two-site observables, and we also investigate the decay of two-time correlations. We find that at a large enough temperature, the steady state approaches closely a thermal state, with a relative error below 1% for the inverse temperature estimated from different observables.
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Affiliation(s)
- Mikel Palmero
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - Xiansong Xu
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - Chu Guo
- Zhengzhou Information Science and Technology Institute, Zhengzhou 450004, China
| | - Dario Poletti
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
- Engineering Product Development, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
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26
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Vicentini F, Biella A, Regnault N, Ciuti C. Variational Neural-Network Ansatz for Steady States in Open Quantum Systems. PHYSICAL REVIEW LETTERS 2019; 122:250503. [PMID: 31347877 DOI: 10.1103/physrevlett.122.250503] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2019] [Indexed: 06/10/2023]
Abstract
We present a general variational approach to determine the steady state of open quantum lattice systems via a neural-network approach. The steady-state density matrix of the lattice system is constructed via a purified neural-network Ansatz in an extended Hilbert space with ancillary degrees of freedom. The variational minimization of cost functions associated to the master equation can be performed using a Markov chain Monte Carlo sampling. As a first application and proof of principle, we apply the method to the dissipative quantum transverse Ising model.
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Affiliation(s)
- Filippo Vicentini
- Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques, CNRS, F-75013, Paris, France
| | - Alberto Biella
- Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques, CNRS, F-75013, Paris, France
| | - Nicolas Regnault
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Sorbonne Paris Cité, F-75005, Paris, France
| | - Cristiano Ciuti
- Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques, CNRS, F-75013, Paris, France
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27
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Hartmann MJ, Carleo G. Neural-Network Approach to Dissipative Quantum Many-Body Dynamics. PHYSICAL REVIEW LETTERS 2019; 122:250502. [PMID: 31347862 DOI: 10.1103/physrevlett.122.250502] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2019] [Indexed: 06/10/2023]
Abstract
In experimentally realistic situations, quantum systems are never perfectly isolated and the coupling to their environment needs to be taken into account. Often, the effect of the environment can be well approximated by a Markovian master equation. However, solving this master equation for quantum many-body systems becomes exceedingly hard due to the high dimension of the Hilbert space. Here we present an approach to the effective simulation of the dynamics of open quantum many-body systems based on machine-learning techniques. We represent the mixed many-body quantum states with neural networks in the form of restricted Boltzmann machines and derive a variational Monte Carlo algorithm for their time evolution and stationary states. We document the accuracy of the approach with numerical examples for a dissipative spin lattice system.
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Affiliation(s)
- Michael J Hartmann
- Institute of Photonics and Quantum Sciences, Heriot-Watt University Edinburgh EH14 4AS, United Kingdom
- Google Research, Erika-Mann-Str. 33, 80636 München, Germany
- Department of Physics, University of Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany
| | - Giuseppe Carleo
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
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28
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Nagy A, Savona V. Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems. PHYSICAL REVIEW LETTERS 2019; 122:250501. [PMID: 31347886 DOI: 10.1103/physrevlett.122.250501] [Citation(s) in RCA: 41] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2019] [Indexed: 06/10/2023]
Abstract
The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom (d.o.f.) is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge posed by this task lies in the complexity of the density matrix increasing exponentially with the system size. Here, we develop a variational method to efficiently simulate the nonequilibrium steady state of Markovian open quantum systems based on variational Monte Carlo methods and on a neural network representation of the density matrix. Thanks to the stochastic reconfiguration scheme, the application of the variational principle is translated into the actual integration of the quantum master equation. We test the effectiveness of the method by modeling the two-dimensional dissipative XYZ spin model on a lattice.
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Affiliation(s)
- Alexandra Nagy
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland
| | - Vincenzo Savona
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland
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29
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Puel TO, Chesi S, Kirchner S, Ribeiro P. Mixed-Order Symmetry-Breaking Quantum Phase Transition Far from Equilibrium. PHYSICAL REVIEW LETTERS 2019; 122:235701. [PMID: 31298904 DOI: 10.1103/physrevlett.122.235701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2018] [Indexed: 06/10/2023]
Abstract
We study the current-carrying steady state of a transverse field Ising chain coupled to magnetic thermal reservoirs and obtain the nonequilibrium phase diagram as a function of the magnetization potential of the reservoirs. Upon increasing the magnetization bias we observe a discontinuous jump of the magnetic order parameter that coincides with a divergence of the correlation length. For steady states with a nonvanishing conductance, the entanglement entropy at zero temperature displays a bias dependent logarithmic correction that violates the area law and differs from the well-known equilibrium case. Our findings show that out-of-equilibrium conditions allow for novel critical phenomena not possible at equilibrium.
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Affiliation(s)
- T O Puel
- Beijing Computational Science Research Center, Beijing 100193, China
- CeFEMA, Instituto Superior Técnico, Universidade de Lisboa Av. Rovisco Pais, 1049-001 Lisboa, Portugal
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
- Zhejiang Province Key Laboratory of Quantum Technology and Devices, Zhejiang University, Hangzhou 310027, China
| | - Stefano Chesi
- Beijing Computational Science Research Center, Beijing 100193, China
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - S Kirchner
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
- Zhejiang Province Key Laboratory of Quantum Technology and Devices, Zhejiang University, Hangzhou 310027, China
| | - P Ribeiro
- Beijing Computational Science Research Center, Beijing 100193, China
- CeFEMA, Instituto Superior Técnico, Universidade de Lisboa Av. Rovisco Pais, 1049-001 Lisboa, Portugal
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30
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Ribeiro P, Prosen T. Integrable Quantum Dynamics of Open Collective Spin Models. PHYSICAL REVIEW LETTERS 2019; 122:010401. [PMID: 31012705 DOI: 10.1103/physrevlett.122.010401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2018] [Indexed: 06/09/2023]
Abstract
We consider a collective quantum spin s in contact with Markovian spin-polarized baths. Using a conserved superoperator charge, a differential representation of the Liouvillian is constructed to find its exact spectrum and eigenmodes. We study the spectral properties of the model in the large-s limit using a semiclassical quantization condition and show that the spectral density may diverge along certain curves in the complex plane. We exploit our exact solution to characterize steady-state properties, in particular at the discontinuous phase transition that arises for unpolarized environments, and to determine the decay rates of coherences and populations. Our approach provides a systematic way of finding integrable Liouvillian operators with nontrivial steady states as well as a way to study their spectral properties and eigenmodes.
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Affiliation(s)
- Pedro Ribeiro
- CeFEMA, Instituto Superior Técnico, Universidade de Lisboa Av. Rovisco Pais, 1049-001 Lisboa, Portugal
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Tomaž Prosen
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
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31
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Vanicat M, Zadnik L, Prosen T. Integrable Trotterization: Local Conservation Laws and Boundary Driving. PHYSICAL REVIEW LETTERS 2018; 121:030606. [PMID: 30085792 DOI: 10.1103/physrevlett.121.030606] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2017] [Revised: 04/18/2018] [Indexed: 06/08/2023]
Abstract
We discuss a general procedure to construct an integrable real-time Trotterization of interacting lattice models. As an illustrative example, we consider a spin-1/2 chain, with continuous time dynamics described by the isotropic (XXX) Heisenberg Hamiltonian. For periodic boundary conditions, local conservation laws are derived from an inhomogeneous transfer matrix, and a boost operator is constructed. In the continuous time limit, these local charges reduce to the known integrals of motion of the Heisenberg chain. In a simple Kraus representation, we also examine the nonequilibrium setting, where our integrable cellular automaton is driven by stochastic processes at the boundaries. We show explicitly how an exact nonequilibrium steady-state density matrix can be written in terms of a staggered matrix product ansatz, and we propose quasilocal conservation laws for the model with periodic boundary conditions. This simple Trotterization scheme, in particular in the open system framework, could prove to be a useful tool for experimental simulations of the lattice models in terms of trapped ion and atom optics setups.
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Affiliation(s)
- Matthieu Vanicat
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
| | - Lenart Zadnik
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
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32
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Balachandran V, Benenti G, Pereira E, Casati G, Poletti D. Perfect Diode in Quantum Spin Chains. PHYSICAL REVIEW LETTERS 2018; 120:200603. [PMID: 29864301 DOI: 10.1103/physrevlett.120.200603] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2017] [Revised: 02/07/2018] [Indexed: 06/08/2023]
Abstract
We study the rectification of the spin current in XXZ chains segmented in two parts, each with a different anisotropy parameter. Using exact diagonalization and a matrix product state algorithm, we find that a large rectification (of the order of 10^{4}) is attainable even using a short chain of N=8 spins, when one-half of the chain is gapless while the other has a large enough anisotropy. We present evidence of diffusive transport when the current is driven in one direction and of a transition to an insulating behavior of the system when driven in the opposite direction, leading to a perfect diode in the thermodynamic limit. The above results are explained in terms of matching of the spectrum of magnon excitations between the two halves of the chain.
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Affiliation(s)
- Vinitha Balachandran
- EPD Pillar, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - Giuliano Benenti
- Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
- NEST, Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Emmanuel Pereira
- Departamento de Física-Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, CP 702, 30.161-970 Belo Horizonte MG, Brazil
| | - Giulio Casati
- Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- International Institute of Physics, Federal University of Rio Grande do Norte, Campus Universitário-Lagoa Nova, Caixa Postale 1613, Natal, Rio Grande Do Norte 59078-970, Brazil
| | - Dario Poletti
- EPD Pillar, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
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33
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Foss-Feig M, Young JT, Albert VV, Gorshkov AV, Maghrebi MF. Solvable Family of Driven-Dissipative Many-Body Systems. PHYSICAL REVIEW LETTERS 2017; 119:190402. [PMID: 29219530 PMCID: PMC6467283 DOI: 10.1103/physrevlett.119.190402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2017] [Indexed: 05/28/2023]
Abstract
Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.
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Affiliation(s)
- Michael Foss-Feig
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Jeremy T Young
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Victor V Albert
- Yale Quantum Institute and Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Mohammad F Maghrebi
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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34
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Carollo F, Garrahan JP, Lesanovsky I, Pérez-Espigares C. Fluctuating hydrodynamics, current fluctuations, and hyperuniformity in boundary-driven open quantum chains. Phys Rev E 2017; 96:052118. [PMID: 29347714 DOI: 10.1103/physreve.96.052118] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2017] [Indexed: 06/07/2023]
Abstract
We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents. In particular, this permits us to show that fermionic open chains display a third-order dynamical phase transition in LD functions. We show that this transition is manifested in a singular change in the structure of trajectories: while typical trajectories are diffusive, rare trajectories associated with atypical currents are ballistic and hyperuniform in their spatial structure. We confirm these results by numerically simulating ensembles of rare trajectories via the cloning method, and by exact numerical diagonalization of the microscopic quantum generator.
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Affiliation(s)
- Federico Carollo
- School of Physics and Astronomy, Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Juan P Garrahan
- School of Physics and Astronomy, Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Igor Lesanovsky
- School of Physics and Astronomy, Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Carlos Pérez-Espigares
- School of Physics and Astronomy, Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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35
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Lemos HCF, Prosen T. Convergence radius of perturbative Lindblad-driven nonequilibrium steady states. Phys Rev E 2017; 95:042137. [PMID: 28505750 DOI: 10.1103/physreve.95.042137] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2017] [Indexed: 11/07/2022]
Abstract
We address the problem of analyzing the radius of convergence of perturbative expansion of nonequilibrium steady states of Lindblad-driven spin chains. A simple formal approach is developed for systematically computing the perturbative expansion of small driven systems. We consider the paradigmatic model of an open XXZ spin-1/2 chain with boundary-supported ultralocal Lindblad dissipators and treat two different perturbative cases: (i) expansion in the system-bath coupling parameter and (ii) expansion in the driving (bias) parameter. In the first case (i) we find that the radius of convergence quickly shrinks with increasing the system size, while in the second case (ii) we find that the convergence radius is always larger than 1, and in particular it approaches 1 from above as we change the anisotropy from an easy-plane (XY) to an easy-axis (Ising) regime.
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Affiliation(s)
- Humberto C F Lemos
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia.,Departamento de Física e Matemática, CAP-Universidade Federal de São João del-Rei, 36.420-000, Ouro Branco, Minas Gerais, Brazil
| | - Tomaž Prosen
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
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36
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Buča B, Prosen T. Charge and spin current statistics of the open Hubbard model with weak coupling to the environment. Phys Rev E 2017; 95:052141. [PMID: 28618579 DOI: 10.1103/physreve.95.052141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2017] [Indexed: 06/07/2023]
Abstract
Based on generalization and extension of our previous work [Phys. Rev. Lett. 112, 067201 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.067201] to multiple independent Markovian baths we will compute the charge and spin current statistics of the open Hubbard model with weak system-bath coupling up to next-to-leading order in the coupling parameter. Only the next-to-leading and higher orders depend on the Hubbard interaction parameter. The physical results are related to those for the XXZ model in the analogous setup implying a certain universality, which potentially holds in this class of nonequilibrium models.
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Affiliation(s)
- Berislav Buča
- Department of Medical Physics and Biophysics, University of Split School of Medicine, 21000 Split, Croatia
| | - Tomaž Prosen
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
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37
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Santos JP, Landi GT. Microscopic theory of a nonequilibrium open bosonic chain. Phys Rev E 2016; 94:062143. [PMID: 28085332 DOI: 10.1103/physreve.94.062143] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2016] [Indexed: 06/06/2023]
Abstract
Quantum master equations form an important tool in the description of transport problems in open quantum systems. However, they suffer from the difficulty that the shape of the Lindblad dissipator depends sensibly on the system Hamiltonian. Consequently, most of the work done in this field has focused on phenomenological dissipators which act locally on different parts of the system. In this paper we show how to construct Lindblad dissipators to model a one-dimensional bosonic tight-binding chain connected to two baths at the first and last site, kept at different temperatures and chemical potentials. We show that even though the bath coupling is local, the effective Lindblad dissipator stemming from this interaction is inherently nonlocal, affecting all normal modes of the system. We then use this formalism to study the current of particles and energy through the system and find that they have the structure of Landauer's formula, with the bath spectral density playing the role of the transfer integral. Finally, we consider infinitesimal temperature and chemical potential gradients and show that the currents satisfy Onsager's reciprocal relations, which is a consequence of the fact that the microscopic quantum dynamics obeys detailed balance.
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Affiliation(s)
- Jader P Santos
- Universidade Federal do ABC, 09210-580 Santo André, Brazil
| | - Gabriel T Landi
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
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38
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Medvedyeva MV, Essler FHL, Prosen T. Exact Bethe Ansatz Spectrum of a Tight-Binding Chain with Dephasing Noise. PHYSICAL REVIEW LETTERS 2016; 117:137202. [PMID: 27715082 DOI: 10.1103/physrevlett.117.137202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2016] [Indexed: 06/06/2023]
Abstract
We construct an exact map between a tight-binding model on any bipartite lattice in the presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the nonequilibrium steady state and the leading decay modes describing the relaxation at late times are related to the η-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model.
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Affiliation(s)
- Mariya V Medvedyeva
- Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana 1000, Slovenia
| | - Fabian H L Essler
- The Rudolf Peierls Centre for Theoretical Physics, Oxford University, Oxford OX1 3NP, United Kingdom
| | - Tomaž Prosen
- Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana 1000, Slovenia
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39
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Guimarães PH, Landi GT, de Oliveira MJ. Nonequilibrium quantum chains under multisite Lindblad baths. Phys Rev E 2016; 94:032139. [PMID: 27739825 DOI: 10.1103/physreve.94.032139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2016] [Indexed: 06/06/2023]
Abstract
We study a quantum XX chain coupled to two heat reservoirs that act on multiple sites and are kept at different temperatures and chemical potentials. The baths are described by Lindblad dissipators, which are constructed by direct coupling to the fermionic normal modes of the chain. Using a perturbative method, we are able to find analytical formulas for all steady-state properties of the system. We compute both the particle or magnetization current and the energy current, both of which are found to have the structure of Landauer's formula. We also obtain exact formulas for the Onsager coefficients. All properties are found to differ substantially from those of a single-site bath. In particular, we find a strong dependence on the intensity of the bath couplings. In the weak-coupling regime, we show that the Onsager reciprocal relations are satisfied.
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Affiliation(s)
- Pedro H Guimarães
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
| | | | - Mario J de Oliveira
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
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40
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Werner AH, Jaschke D, Silvi P, Kliesch M, Calarco T, Eisert J, Montangero S. Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2016; 116:237201. [PMID: 27341253 DOI: 10.1103/physrevlett.116.237201] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2015] [Indexed: 06/06/2023]
Abstract
Open quantum many-body systems play an important role in quantum optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behavior, for various open quantum systems ranging from few to many bodies.
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Affiliation(s)
- A H Werner
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - D Jaschke
- Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - P Silvi
- Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany
| | - M Kliesch
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - T Calarco
- Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - S Montangero
- Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany
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41
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Vorberg D, Wustmann W, Schomerus H, Ketzmerick R, Eckardt A. Nonequilibrium steady states of ideal bosonic and fermionic quantum gases. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062119. [PMID: 26764644 DOI: 10.1103/physreve.92.062119] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2015] [Indexed: 06/05/2023]
Abstract
We investigate nonequilibrium steady states of driven-dissipative ideal quantum gases of both bosons and fermions. We focus on systems of sharp particle number that are driven out of equilibrium either by the coupling to several heat baths of different temperature or by time-periodic driving in combination with the coupling to a heat bath. Within the framework of (Floquet-)Born-Markov theory, several analytical and numerical methods are described in detail. This includes a mean-field theory in terms of occupation numbers, an augmented mean-field theory taking into account also nontrivial two-particle correlations, and quantum-jump-type Monte Carlo simulations. For the case of the ideal Fermi gas, these methods are applied to simple lattice models and the possibility of achieving exotic states via bath engineering is pointed out. The largest part of this work is devoted to bosonic quantum gases and the phenomenon of Bose selection, a nonequilibrium generalization of Bose condensation, where multiple single-particle states are selected to acquire a large occupation [Phys. Rev. Lett. 111, 240405 (2013)]. In this context, among others, we provide a theory for transitions where the set of selected states changes, describe an efficient algorithm for finding the set of selected states, investigate beyond-mean-field effects, and identify the dominant mechanisms for heat transport in the Bose-selected state.
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Affiliation(s)
- Daniel Vorberg
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Waltraut Wustmann
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
| | - Henning Schomerus
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Roland Ketzmerick
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
| | - André Eckardt
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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42
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Barra F. The thermodynamic cost of driving quantum systems by their boundaries. Sci Rep 2015; 5:14873. [PMID: 26445899 PMCID: PMC4597202 DOI: 10.1038/srep14873] [Citation(s) in RCA: 100] [Impact Index Per Article: 11.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2015] [Accepted: 09/10/2015] [Indexed: 11/18/2022] Open
Abstract
The laws of thermodynamics put limits to the efficiencies of thermal machines. Analogues of these laws are now established for quantum engines weakly and passively coupled to the environment providing a framework to find improvements to their performance. Systems whose interaction with the environment is actively controlled do not fall in that framework. Here we consider systems actively and locally coupled to the environment, evolving with a so-called boundary-driven Lindblad equation. Starting from a unitary description of the system plus the environment we simultaneously obtain the Lindblad equation and the appropriate expressions for heat, work and entropy-production of the system extending the framework for the analysis of new, and some already proposed, quantum heat engines. We illustrate our findings in spin 1/2 chains and explain why an XX chain coupled in this way to a single heat bath relaxes to thermodynamic-equilibrium while and XY chain does not. Additionally, we show that an XX chain coupled to a left and a right heat baths behaves as a quantum engine, a heater or refrigerator depending on the parameters, with efficiencies bounded by Carnot efficiencies.
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Affiliation(s)
- Felipe Barra
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago Chile
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43
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Žnidarič M. Relaxation times of dissipative many-body quantum systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042143. [PMID: 26565204 DOI: 10.1103/physreve.92.042143] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2015] [Indexed: 06/05/2023]
Abstract
We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap cannot be larger than ∼1/L. In integrable systems with boundary dissipation one typically observes scaling of ∼1/L(3), while in chaotic ones one can have faster relaxation with the gap scaling as ∼1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.
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Affiliation(s)
- Marko Žnidarič
- Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
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44
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Mierzejewski M, Prelovšek P, Prosen T. Identifying local and quasilocal conserved quantities in integrable systems. PHYSICAL REVIEW LETTERS 2015; 114:140601. [PMID: 25910103 DOI: 10.1103/physrevlett.114.140601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2014] [Indexed: 06/04/2023]
Abstract
We outline a procedure for counting and identifying a complete set of local and quasilocal conserved operators in integrable lattice systems. The method yields a systematic generation of all independent, conserved quasilocal operators related to the time average of local operators with a support on up to M consecutive sites. As an example, we study the anisotropic Heisenberg spin-1/2 chain and show that the number of independent conserved operators grows linearly with M. In addition to the known local operators, there exist novel quasilocal conserved quantities in all the parity sectors. The existence of quasilocal conserved operators is shown also for the isotropic Heisenberg model. Implications for the anomalous relaxation of quenched systems are discussed as well.
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Affiliation(s)
| | - Peter Prelovšek
- Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
- J. Stefan Institute, SI-1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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45
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Popkov V, Prosen T. Infinitely dimensional lax structure for the one-dimensional Hubbard model. PHYSICAL REVIEW LETTERS 2015; 114:127201. [PMID: 25860769 DOI: 10.1103/physrevlett.114.127201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2015] [Indexed: 06/04/2023]
Abstract
We report a two-parametric irreducible infinitely dimensional representation of the Lax integrability condition for the Fermi Hubbard chain. In addition to being of fundamental interest, hinting at possible novel quantum symmetry of the model, our construction allows for an explicit representation of an exact steady state many-body density operator for a nonequilibrium boundary-driven Hubbard chain with arbitrary (asymmetric) particle source (sink) rates at the left (right) end of the chain and with arbitrary boundary values of chemical potentials.
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Affiliation(s)
- Vladislav Popkov
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
- CSDC Università di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
| | - Tomaž Prosen
- Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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Landi GT, Novais E, de Oliveira MJ, Karevski D. Flux rectification in the quantum XXZ chain. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042142. [PMID: 25375473 DOI: 10.1103/physreve.90.042142] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2014] [Indexed: 06/04/2023]
Abstract
Thermal rectification is the phenomenon by which the flux of heat depends on the direction of the flow. It has attracted much interest in recent years due to the possibility of devising thermal diodes. In this paper, we consider the rectification phenomenon in the quantum XXZ chain subject to an inhomogeneous field. The chain is driven out of equilibrium by the contact at its boundaries with two different reservoirs, leading to a constant flow of magnetization from one bath to the other. The nonunitary dynamics of this system, which is modeled by a Lindblad master equation, is treated exactly for small sizes and numerically for larger ones. The functional dependence of the rectification coefficient on the model parameters (anisotropy, field amplitude, and out of equilibrium driving strength) is investigated in full detail. Close to the XX point and at small inhomogeneity and low driving, we have found an explicit expression for the rectification coefficient that is valid at all system sizes. In particular, it shows that the phenomenon of rectification persists even in the thermodynamic limit. Finally, we prove that in the case of the XX chain, there is no rectification.
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Affiliation(s)
| | - E Novais
- Universidade Federal do ABC, 09210-580 Santo André, Brazil
| | | | - Dragi Karevski
- Université de Lorraine, Institut Jean Lamour, Vandoeuvre lès Nancy F-54506, France and CNRS, UMR 7198, IJL, Groupe de Physique Statistique, Nancy, France
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Mierzejewski M, Prelovšek P, Prosen T. Breakdown of the generalized Gibbs ensemble for current-generating quenches. PHYSICAL REVIEW LETTERS 2014; 113:020602. [PMID: 25062158 DOI: 10.1103/physrevlett.113.020602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2014] [Indexed: 06/03/2023]
Abstract
We establish a relation between two hallmarks of integrable systems: the relaxation towards the generalized Gibbs ensemble (GGE) and the dissipationless charge transport. We show that the former one is possible only if the so-called Mazur bound on the charge stiffness is saturated by local conserved quantities. As an example we show how a non-GGE steady state with a current can be generated in the one-dimensional model of interacting spinless fermions with a flux quench. Moreover, an extended GGE involving the quasilocal conserved quantities can be formulated for this case.
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Affiliation(s)
| | - Peter Prelovšek
- Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia and J. Stefan Institute, SI-1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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Buča B, Prosen T. Exactly solvable counting statistics in open weakly coupled interacting spin systems. PHYSICAL REVIEW LETTERS 2014; 112:067201. [PMID: 24580705 DOI: 10.1103/physrevlett.112.067201] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2013] [Indexed: 06/03/2023]
Abstract
We study the full counting statistics for interacting quantum many-body spin systems weakly coupled to the environment. In the leading order in the system-bath coupling, we derive exact spin current statistics for a large class of parity symmetric spin-1/2 systems driven by a pair of Markovian baths with local coupling operators. Interestingly, in this class of systems the leading-order current statistics are universal and do not depend on details of the Hamiltonian. Furthermore, in the specific case of a symmetrically boundary driven anisotropic Heisenberg (XXZ) spin-1/2 chain, we explicitly derive the third-order nonlinear corrections to the current statistics.
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Affiliation(s)
- Berislav Buča
- Department of Physics, FMF, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Department of Physics, FMF, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
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Prosen T. Exact nonequilibrium steady state of an open Hubbard chain. PHYSICAL REVIEW LETTERS 2014; 112:030603. [PMID: 24484128 DOI: 10.1103/physrevlett.112.030603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2013] [Indexed: 06/03/2023]
Abstract
We discuss the current carrying nonequilibrium steady state of an open fermionic Hubbard chain that is strongly driven by Markovian incoherent processes localized at the chain ends. An explicit form of an exact many-body density operator for any value of the coupling parameter is presented. The structure of a matrix product form of the solution is encoded in terms of a novel diagrammatic technique that should allow for generalization to other integrable nonequilibrium models.
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Affiliation(s)
- Tomaž Prosen
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
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Prosen T. Lower bounds on high-temperature diffusion constants from quadratically extensive almost-conserved operators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012142. [PMID: 24580207 DOI: 10.1103/physreve.89.012142] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2013] [Indexed: 06/03/2023]
Abstract
We prove a general theorem which provides a strict lower bound on high-temperature Green-Kubo diffusion constants in locally interacting quantum lattice systems, under the assumption of existence of a quadratically extensive almost conserved quantity: an operator whose commutator with the lattice Hamiltonian is localized on the boundary sites only. We explicitly demonstrate and compute such a bound in two important models in one dimension: in the (isotropic) Heisenberg spin 1/2 chain and in the fermionic Hubbard chain.
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Affiliation(s)
- Tomaž Prosen
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
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