1
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Ferreira J, Jin T, Mannhart J, Giamarchi T, Filippone M. Transport and Nonreciprocity in Monitored Quantum Devices: An Exact Study. PHYSICAL REVIEW LETTERS 2024; 132:136301. [PMID: 38613271 DOI: 10.1103/physrevlett.132.136301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Revised: 01/03/2024] [Accepted: 01/25/2024] [Indexed: 04/14/2024]
Abstract
We study noninteracting fermionic systems undergoing continuous monitoring and driven by biased reservoirs. Averaging over the measurement outcomes, we derive exact formulas for the particle and heat flows in the system. We show that these currents feature competing elastic and inelastic components, which depend nontrivially on the monitoring strength γ. We highlight that monitor-induced inelastic processes lead to nonreciprocal currents, allowing one to extract work from measurements without active feedback control. We illustrate our formalism with two distinct monitoring schemes providing measurement-induced power or cooling. Optimal performances are found for values of the monitoring strength γ, which are hard to address with perturbative approaches.
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Affiliation(s)
- João Ferreira
- Department of Quantum Matter Physics, École de Physique University of Geneva, 1211 Geneva, Switzerland
| | - Tony Jin
- Department of Quantum Matter Physics, École de Physique University of Geneva, 1211 Geneva, Switzerland
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Jochen Mannhart
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Thierry Giamarchi
- Department of Quantum Matter Physics, École de Physique University of Geneva, 1211 Geneva, Switzerland
| | - Michele Filippone
- IRIG-MEM-L_Sim, Université Grenoble Alpes, CEA, Grenoble INP, Grenoble 38000, France
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2
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Kawabata K, Sohal R, Ryu S. Lieb-Schultz-Mattis Theorem in Open Quantum Systems. PHYSICAL REVIEW LETTERS 2024; 132:070402. [PMID: 38427890 DOI: 10.1103/physrevlett.132.070402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Revised: 10/26/2023] [Accepted: 01/18/2024] [Indexed: 03/03/2024]
Abstract
The Lieb-Schultz-Mattis (LSM) theorem provides a general constraint on quantum many-body systems and plays a significant role in the Haldane gap phenomena and topological phases of matter. Here, we extend the LSM theorem to open quantum systems and establish a general theorem that restricts the steady state and spectral gap of Liouvillians based solely on symmetry. Specifically, we demonstrate that the unique gapped steady state is prohibited when translation invariance and U(1) symmetry are simultaneously present for noninteger filling numbers. As an illustrative example, we find that no dissipative gap is open in the spin-1/2 dissipative Heisenberg model, while a dissipative gap can be open in the spin-1 counterpart-an analog of the Haldane gap phenomena in open quantum systems. Furthermore, we show that the LSM constraint manifests itself in a quantum anomaly of the dissipative form factor of Liouvillians. We also find the LSM constraints due to symmetry intrinsic to open quantum systems, such as Kubo-Martin-Schwinger symmetry. Our work leads to a unified understanding of phases and phenomena in open quantum systems.
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Affiliation(s)
- Kohei Kawabata
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Ramanjit Sohal
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Shinsei Ryu
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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3
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Catalano AG, Mattiotti F, Dubail J, Hagenmüller D, Prosen T, Franchini F, Pupillo G. Anomalous Diffusion in the Long-Range Haken-Strobl-Reineker Model. PHYSICAL REVIEW LETTERS 2023; 131:053401. [PMID: 37595217 DOI: 10.1103/physrevlett.131.053401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Accepted: 07/17/2023] [Indexed: 08/20/2023]
Abstract
We analyze the propagation of excitons in a d-dimensional lattice with power-law hopping ∝1/r^{α} in the presence of dephasing, described by a generalized Haken-Strobl-Reineker model. We show that in the strong dephasing (quantum Zeno) regime the dynamics is described by a classical master equation for an exclusion process with long jumps. In this limit, we analytically compute the spatial distribution, whose shape changes at a critical value of the decay exponent α_{cr}=(d+2)/2. The exciton always diffuses anomalously: a superdiffusive motion is associated to a Lévy stable distribution with long-range algebraic tails for α≤α_{cr}, while for α>α_{cr} the distribution corresponds to a surprising mixed Gaussian profile with long-range algebraic tails, leading to the coexistence of short-range diffusion and long-range Lévy flights. In the many-exciton case, we demonstrate that, starting from a domain-wall exciton profile, algebraic tails appear in the distributions for any α, which affects thermalization: the longer the hopping range, the faster equilibrium is reached. Our results are directly relevant to experiments with cold trapped ions, Rydberg atoms, and supramolecular dye aggregates. They provide a way to realize an exclusion process with long jumps experimentally.
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Affiliation(s)
- A G Catalano
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France
- Institut Ruđer Bošković, Bijenička cesta 54, 10000 Zagreb, Croatia
| | - F Mattiotti
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France
| | - J Dubail
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France
- Université de Lorraine and CNRS, LPCT (UMR 7019), 54000 Nancy, France
| | - D Hagenmüller
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France
| | - T Prosen
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
| | - F Franchini
- Institut Ruđer Bošković, Bijenička cesta 54, 10000 Zagreb, Croatia
| | - G Pupillo
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France
- Institut Universitaire de France (IUF), 75000 Paris, France
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4
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Starchl E, Sieberer LM. Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain. PHYSICAL REVIEW LETTERS 2022; 129:220602. [PMID: 36493426 DOI: 10.1103/physrevlett.129.220602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 10/31/2022] [Indexed: 06/17/2023]
Abstract
The construction of the generalized Gibbs ensemble, to which isolated integrable quantum many-body systems relax after a quantum quench, is based upon the principle of maximum entropy. In contrast, there are no universal and model-independent laws that govern the relaxation dynamics and stationary states of open quantum systems, which are subjected to Markovian drive and dissipation. Yet, as we show, relaxation of driven-dissipative systems after a quantum quench can, in fact, be determined by a maximum entropy ensemble, if the Liouvillian that generates the dynamics of the system has parity-time symmetry. Focusing on the specific example of a driven-dissipative Kitaev chain, we show that, similar to isolated integrable systems, the approach to a parity-time symmetric generalized Gibbs ensemble becomes manifest in the relaxation of local observables and the dynamics of subsystem entropies. In contrast, the directional pumping of fermion parity, which is induced by nontrivial non-Hermitian topology of the Kitaev chain, represents a phenomenon that is unique to relaxation dynamics in driven-dissipative systems. Upon increasing the strength of dissipation, parity-time symmetry is broken at a finite critical value, which thus constitutes a sharp dynamical transition that delimits the applicability of the principle of maximum entropy. We show that these results, which we obtain for the specific example of the Kitaev chain, apply to broad classes of noninteracting fermionic models, and we discuss their generalization to a noninteracting bosonic model and an interacting spin chain.
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Affiliation(s)
- Elias Starchl
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
| | - Lukas M Sieberer
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
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5
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Wellnitz D, Preisser G, Alba V, Dubail J, Schachenmayer J. Rise and Fall, and Slow Rise Again, of Operator Entanglement under Dephasing. PHYSICAL REVIEW LETTERS 2022; 129:170401. [PMID: 36332243 DOI: 10.1103/physrevlett.129.170401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2022] [Accepted: 09/20/2022] [Indexed: 06/16/2023]
Abstract
The operator space entanglement entropy, or simply "operator entanglement" (OE), is an indicator of the complexity of quantum operators and of their approximability by matrix product operators (MPOs). We study the OE of the density matrix of 1D many-body models undergoing dissipative evolution. It is expected that, after an initial linear growth reminiscent of unitary quench dynamics, the OE should be suppressed by dissipative processes as the system evolves to a simple stationary state. Surprisingly, we find that this scenario breaks down for one of the most fundamental dissipative mechanisms: dephasing. Under dephasing, after the initial "rise and fall," the OE can rise again, increasing logarithmically at long times. Using a combination of MPO simulations for chains of infinite length and analytical arguments valid for strong dephasing, we demonstrate that this growth is inherent to a U(1) conservation law. We argue that in an XXZ spin model and a Bose-Hubbard model the OE grows universally as 1/4log_{2}t at long times and as 1/2log_{2}t for a Fermi-Hubbard model. We trace this behavior back to anomalous classical diffusion processes.
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Affiliation(s)
- D Wellnitz
- ISIS (UMR 7006) and CESQ, CNRS and Université de Strasbourg, 67000 Strasbourg, France
- IPCMS (UMR 7504), CNRS, 67000 Strasbourg, France
| | - G Preisser
- ISIS (UMR 7006) and CESQ, CNRS and Université de Strasbourg, 67000 Strasbourg, France
| | - V Alba
- Dipartimento di Fisica, Università di Pisa, and INFN Sezione di Pisa, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy
| | - J Dubail
- ISIS (UMR 7006) and CESQ, CNRS and Université de Strasbourg, 67000 Strasbourg, France
- Université de Lorraine, CNRS, LPCT, F-54000 Nancy, France
| | - J Schachenmayer
- ISIS (UMR 7006) and CESQ, CNRS and Université de Strasbourg, 67000 Strasbourg, France
- IPCMS (UMR 7504), CNRS, 67000 Strasbourg, France
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6
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Fujimoto K, Hamazaki R, Kawaguchi Y. Impact of Dissipation on Universal Fluctuation Dynamics in Open Quantum Systems. PHYSICAL REVIEW LETTERS 2022; 129:110403. [PMID: 36154403 DOI: 10.1103/physrevlett.129.110403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 08/08/2022] [Indexed: 06/16/2023]
Abstract
Recent theoretical and experimental works have explored universal dynamics related to surface growth physics in isolated quantum systems. In this Letter, we theoretically elucidate that dissipation drastically alters universal particle-number-fluctuation dynamics associated with surface-roughness growth in one-dimensional free fermions and bosons. In a system under dephasing that causes loss of spatial coherence, we numerically find that a universality class of surface-roughness dynamics changes from the ballistic class to a class with the Edwards-Wilkinson scaling exponents and an unconventional scaling function. We provide the analytical derivation of the diffusion equation from the dephasing Lindblad equation via a renormalization-group technique and succeed in explaining the drastic change. Furthermore, we numerically find the same change of the universality class under a more nontrivial dissipation, i.e., symmetric incoherent hopping.
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Affiliation(s)
- Kazuya Fujimoto
- Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan
| | - Ryusuke Hamazaki
- Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR), RIKEN iTHEMS, Wako, Saitama 351-0198, Japan
| | - Yuki Kawaguchi
- Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan
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7
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McDonald A, Clerk AA. Exact Solutions of Interacting Dissipative Systems via Weak Symmetries. PHYSICAL REVIEW LETTERS 2022; 128:033602. [PMID: 35119876 DOI: 10.1103/physrevlett.128.033602] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2021] [Accepted: 01/05/2022] [Indexed: 06/14/2023]
Abstract
We demonstrate how the presence of continuous weak symmetry can be used to analytically diagonalize the Liouvillian of a class of Markovian dissipative systems with strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method can be viewed as implementing an exact, sector-dependent mean-field decoupling, or alternatively, as a kind of quantum-to-classical mapping. We focus on two canonical examples: a nonlinear bosonic mode subject to incoherent loss and pumping, and an inhomogeneous quantum Ising model with arbitrary connectivity and local dissipation. In both cases, we calculate and analyze the full dissipation spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
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Affiliation(s)
- A McDonald
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - A A Clerk
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
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8
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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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9
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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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10
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Yuan D, Wang HR, Wang Z, Deng DL. Solving the Liouvillian Gap with Artificial Neural Networks. PHYSICAL REVIEW LETTERS 2021; 126:160401. [PMID: 33961454 DOI: 10.1103/physrevlett.126.160401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2020] [Accepted: 03/30/2021] [Indexed: 06/12/2023]
Abstract
We propose a machine-learning inspired variational method to obtain the Liouvillian gap, which plays a crucial role in characterizing the relaxation time and dissipative phase transitions of open quantum systems. By using "spin bi-base mapping," we map the density matrix to a pure restricted-Boltzmann-machine (RBM) state and transform the Liouvillian superoperator to a rank-two non-Hermitian operator. The Liouvillian gap can be obtained by a variational real-time evolution algorithm under this non-Hermitian operator. We apply our method to the dissipative Heisenberg model in both one and two dimensions. For the isotropic case, we find that the Liouvillian gap can be analytically obtained and in one dimension even the whole Liouvillian spectrum can be exactly solved using the Bethe ansatz method. By comparing our numerical results with their analytical counterparts, we show that the Liouvillian gap could be accessed by the RBM approach efficiently to a desirable accuracy, regardless of the dimensionality and entanglement properties.
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Affiliation(s)
- Dong Yuan
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
- Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - He-Ran Wang
- Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China
| | - Zhong Wang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China
| | - Dong-Ling Deng
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
- Shanghai Qi Zhi Institute, 41st Floor, AI Tower, No. 701 Yunjin Road, Xuhui District, Shanghai 200232, China
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11
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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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12
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Bácsi Á, Moca CP, Zaránd G, Dóra B. Vaporization Dynamics of a Dissipative Quantum Liquid. PHYSICAL REVIEW LETTERS 2020; 125:266803. [PMID: 33449736 DOI: 10.1103/physrevlett.125.266803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Accepted: 12/07/2020] [Indexed: 06/12/2023]
Abstract
We investigate the stability of a Luttinger liquid, upon suddenly coupling it to a dissipative environment. Within the Lindblad equation, the environment couples to local currents and heats the quantum liquid up to infinite temperatures. The single particle density matrix reveals the fractionalization of fermionic excitations in the spatial correlations by retaining the initial noninteger power law exponents, accompanied by an exponential decay in time with an interaction dependent rate. The spectrum of the time evolved density matrix is gapped, which collapses gradually as -ln(t). The von Neumann entropy crosses over from the early time -tln(t) behavior to ln(t) growth for late times. The early time dynamics is captured numerically by performing simulations on spinless interacting fermions, using several numerically exact methods. Our results could be tested experimentally in bosonic Luttinger liquids.
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Affiliation(s)
- Ádám Bácsi
- MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
- Department of Mathematics and Computational Sciences, Széchenyi István University, 9026 Győr, Hungary
| | - Cătălin Paşcu Moca
- MTA-BME Quantum Dynamics and Correlations Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
- Department of Physics, University of Oradea, 410087 Oradea, Romania
| | - Gergely Zaránd
- MTA-BME Quantum Dynamics and Correlations Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
- BME-MTA Exotic Quantum Phases Research Group, Department of Theoretical Physics, Budapest University of Technology and Economics, 1521 Budapest, Hungary
| | - Balázs Dóra
- MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
- Department of Theoretical Physics, Budapest University of Technology and Economics, 1521 Budapest, Hungary
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13
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Essler FHL, Piroli L. Integrability of one-dimensional Lindbladians from operator-space fragmentation. Phys Rev E 2020; 102:062210. [PMID: 33466089 DOI: 10.1103/physreve.102.062210] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Accepted: 11/25/2020] [Indexed: 06/12/2023]
Abstract
We introduce families of one-dimensional Lindblad equations describing open many-particle quantum systems that are exactly solvable in the following sense: (i) The space of operators splits into exponentially many (in system size) subspaces that are left invariant under the dissipative evolution; (ii) the time evolution of the density matrix on each invariant subspace is described by an integrable Hamiltonian. The prototypical example is the quantum version of the asymmetric simple exclusion process (ASEP) which we analyze in some detail. We show that in each invariant subspace the dynamics is described in terms of an integrable spin-1/2 XXZ Heisenberg chain with either open or twisted boundary conditions. We further demonstrate that Lindbladians featuring integrable operator-space fragmentation can be found in spin chains with arbitrary local physical dimensions.
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Affiliation(s)
- Fabian H L Essler
- The Rudolf Peierls Centre for Theoretical Physics, Oxford University, Oxford OX1 3PU, United Kingdom
| | - Lorenzo Piroli
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology, Schellingstraße 4, 80799 München, Germany
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14
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15
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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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16
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Bácsi Á, Moca CP, Dóra B. Dissipation-Induced Luttinger Liquid Correlations in a One-Dimensional Fermi Gas. PHYSICAL REVIEW LETTERS 2020; 124:136401. [PMID: 32302153 DOI: 10.1103/physrevlett.124.136401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2019] [Accepted: 03/09/2020] [Indexed: 06/11/2023]
Abstract
We study a one-dimensional Fermi gas in the presence of dissipative coupling to environment through the Lindblad equation. The dissipation involves energy exchange with the environment and favours the relaxation of electrons to excitations. After switching on the dissipation, the system approaches a steady state, which is described by a generalized Gibbs ensemble. The fermionic single particle density matrix resembles deceivingly to that in a hermitian interaction quench. It decays inversely with the distance for short times due to the fermionic correlations in the initial state, which changes into a noninteger power law decay for late times, representing dissipation-induced Luttinger liquid behavior. However, the crossover between the two regions occurs due to dissipation-induced damping, and is unrelated to the propagation of excitations. The velocity of information spreading is set by the dissipative coupling, and differs significantly from the original sound velocity. The thermodynamic entropy grows as -t ln t initially, and saturates to an extensive value. Our results can be tested experimentally in one-dimensional Dirac systems.
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Affiliation(s)
- Ádám Bácsi
- MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
- Department of Mathematics and Computational Sciences, Széchenyi István University, 9026 Győr, Hungary
| | - Cătălin Paşcu Moca
- MTA-BME Quantum Dynamics and Correlations Research Group, Budapest University of Technology and Economics, 1521, Budapest, Hungary
- Department of Physics, University of Oradea, 410087 Oradea, Romania
- Department of Theoretical Physics, Budapest University of Technology and Economics, 1521 Budapest, Hungary
| | - Balázs Dóra
- MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
- Department of Theoretical Physics, Budapest University of Technology and Economics, 1521 Budapest, Hungary
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17
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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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18
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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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19
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Hamazaki R, Kawabata K, Ueda M. Non-Hermitian Many-Body Localization. PHYSICAL REVIEW LETTERS 2019; 123:090603. [PMID: 31524436 DOI: 10.1103/physrevlett.123.090603] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2018] [Indexed: 06/10/2023]
Abstract
Many-body localization is shown to suppress the imaginary parts of complex eigenenergies for general non-Hermitian Hamiltonians having time-reversal symmetry. We demonstrate that a real-complex transition, which we conjecture occurs upon many-body localization, profoundly affects the dynamical stability of non-Hermitian interacting systems with asymmetric hopping that respects time-reversal symmetry. Moreover, the real-complex transition is shown to be absent in non-Hermitian many-body systems with gain and/or loss that breaks time-reversal symmetry, even though the many-body localization transition still persists.
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Affiliation(s)
- Ryusuke Hamazaki
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Kohei Kawabata
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, 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, Wako 351-0198, Japan
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20
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Bernard D, Jin T. Open Quantum Symmetric Simple Exclusion Process. PHYSICAL REVIEW LETTERS 2019; 123:080601. [PMID: 31491217 DOI: 10.1103/physrevlett.123.080601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2019] [Indexed: 06/10/2023]
Abstract
We present the solution to a model of fermions hopping between neighboring sites on a line with random Brownian amplitudes and open boundary conditions driving the system out of equilibrium. The average dynamics reduces to that of the symmetric simple exclusion process. However, the full distribution encodes for a richer behavior, entailing fluctuating quantum coherences which survive in the steady limit. We determine exactly the steady statistical distribution of the system state. We show that the out-of-equilibrium quantum coherence fluctuations satisfy a large-deviation principle, and we present a method to recursively compute exactly the large-deviation function. As a by-product, our approach gives a solution of the classical symmetric simple exclusion process based on fermion technology. Our results open the route towards the extension of the macroscopic fluctuation theory to many-body quantum systems.
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Affiliation(s)
- Denis Bernard
- Laboratoire de Physique de l'Ecole Normale Supérieure de Paris, CNRS, ENS & Université PSL, Sorbonne Université, Université Paris Diderot, 75005 France
| | - Tony Jin
- Laboratoire de Physique de l'Ecole Normale Supérieure de Paris, CNRS, ENS & Université PSL, Sorbonne Université, Université Paris Diderot, 75005 France
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21
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Tonielli F, Fazio R, Diehl S, Marino J. Orthogonality Catastrophe in Dissipative Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2019; 122:040604. [PMID: 30768302 DOI: 10.1103/physrevlett.122.040604] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2018] [Revised: 01/09/2019] [Indexed: 06/09/2023]
Abstract
We present an analog of the phenomenon of orthogonality catastrophe in quantum many-body systems subject to a local dissipative impurity. We show that the fidelity F(t), giving a measure for distance of the time-evolved state from the initial one, displays a universal scaling form F(t)∝t^{θ}e^{-γt}, when the system supports long-range correlations, in a fashion reminiscent of traditional instances of orthogonality catastrophe in condensed matter. An exponential falloff at rate γ signals the onset of environmental decoherence, which is critically slowed down by the additional algebraic contribution to the fidelity. This picture is derived within a second-order cumulant expansion suited for Liouvillian dynamics, and substantiated for the one-dimensional transverse field quantum Ising model subject to a local dephasing jump operator, as well as for XY and XX quantum spin chains, and for the two-dimensional Bose gas deep in the superfluid phase with local particle heating. Our results hint that local sources of dissipation can be used to inspect real-time correlations and to induce a delay of decoherence in open quantum many-body systems.
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Affiliation(s)
- F Tonielli
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
| | - R Fazio
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy and NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - S Diehl
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
| | - J Marino
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
- Department of Physics, Harvard University, Cambridge Massachusetts 02138, USA and Department of Quantum Matter Physics, University of Geneva, 1211 Geneve, Switzerland
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22
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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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23
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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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24
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Rowlands DA, Lamacraft A. Noisy Spins and the Richardson-Gaudin Model. PHYSICAL REVIEW LETTERS 2018; 120:090401. [PMID: 29547309 DOI: 10.1103/physrevlett.120.090401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2017] [Revised: 01/12/2018] [Indexed: 06/08/2023]
Abstract
We study a system of spins (qubits) coupled to a common noisy environment, each precessing at its own frequency. The correlated noise experienced by the spins implies long-lived correlations that relax only due to the differing frequencies. We use a mapping to a non-Hermitian integrable Richardson-Gaudin model to find the exact spectrum of the quantum master equation in the high-temperature limit and, hence, determine the decay rate. Our solution can be used to evaluate the effect of inhomogeneous splittings on a system of qubits coupled to a common bath.
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Affiliation(s)
- Daniel A Rowlands
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Austen Lamacraft
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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