1
|
Kohlert T, Scherg S, Sala P, Pollmann F, Hebbe Madhusudhana B, Bloch I, Aidelsburger M. Exploring the Regime of Fragmentation in Strongly Tilted Fermi-Hubbard Chains. PHYSICAL REVIEW LETTERS 2023; 130:010201. [PMID: 36669215 DOI: 10.1103/physrevlett.130.010201] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Revised: 09/09/2022] [Accepted: 11/17/2022] [Indexed: 06/17/2023]
Abstract
Intriguingly, quantum many-body systems may defy thermalization even without disorder. One example is so-called fragmented models, where the many-body Hilbert space fragments into dynamically disconnected subspaces that are not determined by the global symmetries of the model. In this Letter we demonstrate that the tilted one-dimensional Fermi-Hubbard model naturally realizes distinct effective Hamiltonians that are expected to support nonergodic behavior due to fragmentation, even at resonances between the tilt energy and the Hubbard on site interaction. We find that the effective description captures the observed dynamics in experimentally accessible parameter ranges of moderate tilt values. Specifically, we observe a pronounced dependence of the relaxation dynamics on the initial doublon fraction, which directly reveals the microscopic processes of the fragmented model. Our results pave the way for future studies of nonergodic behavior in higher dimensions.
Collapse
Affiliation(s)
- Thomas Kohlert
- Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Sebastian Scherg
- Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Pablo Sala
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
| | - Frank Pollmann
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
| | - Bharath Hebbe Madhusudhana
- Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Immanuel Bloch
- Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Monika Aidelsburger
- Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 Munich, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| |
Collapse
|
2
|
Giri MK, Mondal S, Das BP, Mishra T. Signatures of Nontrivial Pairing in the Quantum Walk of Two-Component Bosons. PHYSICAL REVIEW LETTERS 2022; 129:050601. [PMID: 35960573 DOI: 10.1103/physrevlett.129.050601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2021] [Revised: 01/16/2022] [Accepted: 07/08/2022] [Indexed: 06/15/2023]
Abstract
Nearest neighbor bosons possessing only on-site interactions do not form on-site bound pairs in their quantum walk due to fermionization. We obtain signatures of nontrivial on-site pairing in the quantum walk of strongly interacting two component bosons in a one dimensional lattice. By considering an initial state with particles from different components located at the nearest-neighbor sites in the central region of the lattice, we show that in the dynamical evolution of the system, competing intra- and intercomponent on-site repulsion leads to the formation of on-site intercomponent bound states. We find that when the total number of particles is three, an intercomponent pair is favored in the limit of equal intra- and intercomponent interaction strengths. However, when two bosons from each species are considered, intercomponent pairs and trimer are favored depending on the ratios of the intra- and intercomponent interactions. In both cases, we find that the quantum walks exhibit a reentrant behavior as a function of intercomponent interaction.
Collapse
Affiliation(s)
- Mrinal Kanti Giri
- Department of Physics, Indian Institute of Technology, Guwahati-781039, India
| | - Suman Mondal
- Department of Physics, Indian Institute of Technology, Guwahati-781039, India
| | - B P Das
- Centre for Quantum Engineering Research and Education, TCG Centres for Research and Education in Science and Technology, Sector V, Salt Lake, Kolkata 70091, India
- Department of Physics, School of Science, Tokyo Institute of Technology, 2-1-2-1-H86, Ookayama, Meguro-ku, Tokyo 152-8550, Japan
| | - Tapan Mishra
- Department of Physics, Indian Institute of Technology, Guwahati-781039, India
- Centre for Quantum Engineering Research and Education, TCG Centres for Research and Education in Science and Technology, Sector V, Salt Lake, Kolkata 70091, India
- National Institute of Science Education and Research, HBNI, Jatni 752050, India
| |
Collapse
|
3
|
Zawadzki K, Skelt AH, D'Amico I. Approximating quantum thermodynamic properties using DFT. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:274002. [PMID: 35405664 DOI: 10.1088/1361-648x/ac6648] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2022] [Accepted: 04/11/2022] [Indexed: 06/14/2023]
Abstract
The fabrication, utilisation, and efficiency of quantum technology devices rely on a good understanding of quantum thermodynamic properties. Many-body systems are often used as hardware for these quantum devices, but interactions between particles make the complexity of related calculations grow exponentially with the system size. Here we explore and systematically compare 'simple' and 'hybrid' approximations to the average work and entropy variation built on static density functional theory concepts. These approximations are computationally cheap and could be applied to large systems. We exemplify them considering driven one-dimensional Hubbard chains and show that, for 'simple' approximations and low to medium temperatures, it pays to consider a good estimate of the Kohn-Sham Hamiltonian to approximate the driving Hamiltonian. Our results confirm that a 'hybrid' approach, requiring a very good approximation of the initial and, for the entropy, final states of the system, provides great improvements. This approach should be particularly efficient when many-body effects are not increased by the driving Hamiltonian.
Collapse
Affiliation(s)
- K Zawadzki
- ICTP South American Institute for Fundamental Research, IFT-UNESP, São Paulo CEP: 01140-070, Brazil
| | - A H Skelt
- Department of Physics, University of York, York YO10 5DD, United Kingdom
| | - I D'Amico
- Department of Physics, University of York, York YO10 5DD, United Kingdom
| |
Collapse
|
4
|
Giri MK, Mondal S, Das BP, Mishra T. Two component quantum walk in one-dimensional lattice with hopping imbalance. Sci Rep 2021; 11:22056. [PMID: 34764349 PMCID: PMC8585883 DOI: 10.1038/s41598-021-01230-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Accepted: 10/12/2021] [Indexed: 11/23/2022] Open
Abstract
We investigate the two-component quantum walk in one-dimensional lattice. We show that the inter-component interaction strength together with the hopping imbalance between the components exhibit distinct features in the quantum walk for different initial states. When the walkers are initially on the same site, both the slow and fast particles perform independent particle quantum walks when the interaction between them is weak. However, stronger inter-particle interactions result in quantum walks by the repulsively bound pair formed between the two particles. For different initial states when the walkers are on different sites initially, the quantum walk performed by the slow particle is almost independent of that of the fast particle, which exhibits reflected and transmitted components across the particle with large hopping strength for weak interactions. Beyond a critical value of the interaction strength, the wave function of the fast particle ceases to penetrate through the slow particle signalling a spatial phase separation. However, when the two particles are initially at the two opposite edges of the lattice, then the interaction facilitates the complete reflection of both of them from each other. We analyze the above mentioned features by examining various physical quantities such as the on-site density evolution, two-particle correlation functions and transmission coefficients.
Collapse
Affiliation(s)
- Mrinal Kanti Giri
- Department of Physics, Indian Institute of Technology, Guwahati, 781039, India
| | - Suman Mondal
- Department of Physics, Indian Institute of Technology, Guwahati, 781039, India
| | - Bhanu Pratap Das
- Centre for Quantum Engineering Research and Education, TCG Centres for Research and Education in Science and Technology, Sector V, Salt Lake, Kolkata, 70091, India. .,Department of Physics, School of Science, Tokyo Institute of Technology, 2-1-2-1-H86 Ookayama Meguro-ku, Tokyo, 152-8550, Japan.
| | - Tapan Mishra
- Department of Physics, Indian Institute of Technology, Guwahati, 781039, India. .,Centre for Quantum Engineering Research and Education, TCG Centres for Research and Education in Science and Technology, Sector V, Salt Lake, Kolkata, 70091, India.
| |
Collapse
|
5
|
Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains. Nat Commun 2021; 12:4490. [PMID: 34301932 PMCID: PMC8302618 DOI: 10.1038/s41467-021-24726-0] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2021] [Accepted: 05/26/2021] [Indexed: 11/09/2022] Open
Abstract
The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.
Collapse
|
6
|
De Nardis J, Gopalakrishnan S, Ilievski E, Vasseur R. Superdiffusion from Emergent Classical Solitons in Quantum Spin Chains. PHYSICAL REVIEW LETTERS 2020; 125:070601. [PMID: 32857584 DOI: 10.1103/physrevlett.125.070601] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
Finite-temperature spin transport in the quantum Heisenberg spin chain is known to be superdiffusive, and has been conjectured to lie in the Kardar-Parisi-Zhang (KPZ) universality class. Using a kinetic theory of transport, we compute the KPZ coupling strength for the Heisenberg chain as a function of temperature, directly from microscopics; the results agree well with density-matrix renormalization group simulations. We establish a rigorous quantum-classical correspondence between the "giant quasiparticles" that govern superdiffusion and solitons in the classical continuous Landau-Lifshitz ferromagnet. We conclude that KPZ universality has the same origin in classical and quantum integrable isotropic magnets: a finite-temperature gas of low-energy classical solitons.
Collapse
Affiliation(s)
- Jacopo De Nardis
- Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium
| | - Sarang Gopalakrishnan
- Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York 10314; Physics Program and Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, New York 10016, USA
| | - Enej Ilievski
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| |
Collapse
|
7
|
Moreno JR, Carleo G, Georges A. Deep Learning the Hohenberg-Kohn Maps of Density Functional Theory. PHYSICAL REVIEW LETTERS 2020; 125:076402. [PMID: 32857556 DOI: 10.1103/physrevlett.125.076402] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2019] [Accepted: 07/14/2020] [Indexed: 06/11/2023]
Abstract
A striking consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of a bijection between the local density and the ground-state many-body wave function. Here we study the problem of constructing approximations to the Hohenberg-Kohn map using a statistical learning approach. Using supervised deep learning with synthetic data, we show that this map can be accurately constructed for a chain of one-dimensional interacting spinless fermions in different phases of this model including the charge ordered Mott insulator and metallic phases and the critical point separating them. However, we also find that the learning is less effective across quantum phase transitions, suggesting an intrinsic difficulty in efficiently learning nonsmooth functional relations. We further study the problem of directly reconstructing complex observables from simple local density measurements, proposing a scheme amenable to statistical learning from experimental data.
Collapse
Affiliation(s)
- Javier Robledo Moreno
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
- Center for Quantum Phenomena, Department of Physics, New York University, 726 Broadway, New York, New York 10003, USA
| | - Giuseppe Carleo
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Antoine Georges
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
- CPHT, CNRS, École Polytechnique, IP Paris, F-91128 Palaiseau, France
- DQMP, Université de Genève, 24 quai Ernest Ansermet, CH-1211 Genève, Suisse
| |
Collapse
|
8
|
Rausch R, Potthoff M, Kawakami N. Magnetic Doublon Bound States in the Kondo Lattice Model. PHYSICAL REVIEW LETTERS 2019; 123:216401. [PMID: 31809148 DOI: 10.1103/physrevlett.123.216401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2019] [Indexed: 06/10/2023]
Abstract
We present a novel pairing mechanism for electrons, mediated by magnons. These paired bound states are termed "magnetic doublons." Applying numerically exact techniques (full diagonalization and the density-matrix renormalization group, DMRG) to the Kondo lattice model at strong exchange coupling J for different fillings and magnetic configurations, we demonstrate that magnetic doublon excitations exist as composite objects with very weak dispersion. They are highly stable, support a novel "inverse" colossal magnetoresistance and potentially other effects.
Collapse
Affiliation(s)
- Roman Rausch
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Michael Potthoff
- Department of Physics, University of Hamburg, Jungiusstraße 9, D-20355 Hamburg, Germany
| | - Norio Kawakami
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| |
Collapse
|
9
|
Anderson R, Wang F, Xu P, Venu V, Trotzky S, Chevy F, Thywissen JH. Conductivity Spectrum of Ultracold Atoms in an Optical Lattice. PHYSICAL REVIEW LETTERS 2019; 122:153602. [PMID: 31050527 DOI: 10.1103/physrevlett.122.153602] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2018] [Indexed: 06/09/2023]
Abstract
We measure the conductivity of neutral fermions in a cubic optical lattice. Using in situ fluorescence microscopy, we observe the alternating current resultant from a single-frequency uniform force applied by displacement of a weak harmonic trapping potential. In the linear response regime, a neutral-particle analog of Ohm's law gives the conductivity as the ratio of total current to force. For various lattice depths, temperatures, interaction strengths, and fillings, we measure both real and imaginary conductivity, up to a frequency sufficient to capture the transport dynamics within the lowest band. The spectral width of the real conductivity reveals the current dissipation rate in the lattice, and the integrated spectral weight is related to thermodynamic properties of the system through a sum rule. The global conductivity decreases with increased band-averaged effective mass, which at high temperatures approaches a T-linear regime. Relaxation of current is observed to require a finite lattice depth, which breaks Galilean invariance and enables damping through collisions between fermions.
Collapse
Affiliation(s)
- Rhys Anderson
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Fudong Wang
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Peihang Xu
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Vijin Venu
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Stefan Trotzky
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Frédéric Chevy
- Laboratoire Kastler Brossel, ENS-PSL Research University, CNRS, UPMC-Sorbonne Université, Collège de France, 24 Rue Lhomond, 75005 Paris, France
| | - Joseph H Thywissen
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1M1 Canada
| |
Collapse
|
10
|
Ilievski E, De Nardis J, Medenjak M, Prosen T. Superdiffusion in One-Dimensional Quantum Lattice Models. PHYSICAL REVIEW LETTERS 2018; 121:230602. [PMID: 30576201 DOI: 10.1103/physrevlett.121.230602] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2018] [Revised: 09/10/2018] [Indexed: 06/09/2023]
Abstract
We identify a class of one-dimensional spin and fermionic lattice models that display diverging spin and charge diffusion constants, including several paradigmatic models of exactly solvable, strongly correlated many-body dynamics such as the isotropic Heisenberg spin chains, the Fermi-Hubbard model, and the t-J model at the integrable point. Using the hydrodynamic transport theory, we derive an analytic lower bound on the spin and charge diffusion constants by calculating the curvature of the corresponding Drude weights at half-filling, and demonstrate that for certain lattice models with isotropic interactions some of the Noether charges exhibit superdiffusive transport at finite temperature and half-filling.
Collapse
Affiliation(s)
- Enej Ilievski
- Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Jacopo De Nardis
- Département de Physique, Ecole Normale Supérieure, PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France
| | - Marko Medenjak
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| |
Collapse
|
11
|
De Nardis J, Bernard D, Doyon B. Hydrodynamic Diffusion in Integrable Systems. PHYSICAL REVIEW LETTERS 2018; 121:160603. [PMID: 30387673 DOI: 10.1103/physrevlett.121.160603] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2018] [Revised: 09/21/2018] [Indexed: 06/08/2023]
Abstract
We show that hydrodynamic diffusion is generically present in many-body, one-dimensional interacting quantum and classical integrable models. We extend the recently developed generalized hydrodynamic (GHD) to include terms of Navier-Stokes type, which leads to positive entropy production and diffusive relaxation mechanisms. These terms provide the subleading diffusive corrections to Euler-scale GHD for the large-scale nonequilibrium dynamics of integrable systems, and arise due to two-body scatterings among quasiparticles. We give exact expressions for the diffusion coefficients. Our results apply to a large class of integrable models, including quantum and classical, Galilean and relativistic field theories, chains, and gases in one dimension, such as the Lieb-Liniger model describing cold atom gases and the Heisenberg quantum spin chain. We provide numerical evaluations in the Heisenberg XXZ spin chain, both for the spin diffusion constant, and for the diffusive effects during the melting of a small domain wall of spins, finding excellent agreement with time-dependent density matrix renormalization group numerical simulations.
Collapse
Affiliation(s)
- Jacopo De Nardis
- Département de Physique, Ecole Normale Supérieure, PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France
| | - Denis Bernard
- Laboratoire de Physique Théorique de l'Ecole Normale Supérieure de Paris, CNRS, ENS, PSL University & Sorbonne Université, 75005 Paris, France
| | - Benjamin Doyon
- Department of Mathematics, King's College London, Strand WC2R 2LS London, United Kingdom
| |
Collapse
|