1
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Royen K, Mondal S, Pollmann F, Heidrich-Meisner F. Enhanced many-body localization in a kinetically constrained model. Phys Rev E 2024; 109:024136. [PMID: 38491625 DOI: 10.1103/physreve.109.024136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2023] [Accepted: 01/23/2024] [Indexed: 03/18/2024]
Abstract
In the study of the thermalization of closed quantum systems, the role of kinetic constraints on the temporal dynamics and the eventual thermalization is attracting significant interest. Kinetic constraints typically lead to long-lived metastable states depending on initial conditions. We consider a model of interacting hardcore bosons with an additional kinetic constraint that was originally devised to capture glassy dynamics at high densities. As a main result, we demonstrate that the system is highly prone to localization in the presence of uncorrelated disorder. Adding disorder quickly triggers long-lived dynamics as evidenced in the time evolution of density autocorrelations. Moreover, the kinetic constraint favors localization also in the eigenstates, where a finite-size transition to a many-body localized phase occurs for much lower disorder strengths than for the same model without a kinetic constraint. Our work sheds light on the intricate interplay of kinetic constraints and localization and may provide additional control over many-body localized phases in the time domain.
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Affiliation(s)
- Karl Royen
- Institut für Theoretische Physik, Georg-August-Universität Göttingen, D-37077 Göttingen, Germany
| | - Suman Mondal
- Institut für Theoretische Physik, Georg-August-Universität Göttingen, D-37077 Göttingen, Germany
| | - Frank Pollmann
- Physics Department, TUM School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Fabian Heidrich-Meisner
- Institut für Theoretische Physik, Georg-August-Universität Göttingen, D-37077 Göttingen, Germany
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2
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Wilming H, Osborne TJ, Decker KSC, Karrasch C. Reviving product states in the disordered Heisenberg chain. Nat Commun 2023; 14:5847. [PMID: 37730793 PMCID: PMC10511451 DOI: 10.1038/s41467-023-41464-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Accepted: 09/01/2023] [Indexed: 09/22/2023] Open
Abstract
When a generic quantum system is prepared in a simple initial condition, it typically equilibrates toward a state that can be described by a thermal ensemble. A known exception is localized systems that are non-ergodic and do not thermalize; however, local observables are still believed to become stationary. Here we demonstrate that this general picture is incomplete by constructing product states that feature periodic high-fidelity revivals of the full wavefunction and local observables that oscillate indefinitely. The system neither equilibrates nor thermalizes. This is analogous to the phenomenon of weak ergodicity breaking due to many-body scars and challenges aspects of the current phenomenology of many-body localization, such as the logarithmic growth of the entanglement entropy. To support our claim, we combine analytic arguments with large-scale tensor network numerics for the disordered Heisenberg chain. Our results hold for arbitrarily long times in chains of 160 sites up to machine precision.
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Affiliation(s)
- Henrik Wilming
- Leibniz Universität Hannover, Appelstraße 2, 30167, Hannover, Germany.
| | - Tobias J Osborne
- Leibniz Universität Hannover, Appelstraße 2, 30167, Hannover, Germany
| | - Kevin S C Decker
- Technische Universität Braunschweig, Institut für Mathematische Physik, Mendelssohnstraße 3, 38106, Braunschweig, Germany
| | - Christoph Karrasch
- Technische Universität Braunschweig, Institut für Mathematische Physik, Mendelssohnstraße 3, 38106, Braunschweig, Germany
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3
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Hopjan M, Vidmar L. Scale-Invariant Survival Probability at Eigenstate Transitions. PHYSICAL REVIEW LETTERS 2023; 131:060404. [PMID: 37625072 DOI: 10.1103/physrevlett.131.060404] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Revised: 04/21/2023] [Accepted: 07/20/2023] [Indexed: 08/27/2023]
Abstract
Understanding quantum phase transitions in highly excited Hamiltonian eigenstates is currently far from being complete. It is particularly important to establish tools for their characterization in time domain. Here, we argue that a scaled survival probability, where time is measured in units of a typical Heisenberg time, exhibits a scale-invariant behavior at eigenstate transitions. We first demonstrate this property in two paradigmatic quadratic models, the one-dimensional Aubry-Andre model and three-dimensional Anderson model. Surprisingly, we then show that similar phenomenology emerges in the interacting avalanche model of ergodicity breaking phase transitions. This establishes an intriguing similarity between localization transition in quadratic systems and ergodicity breaking phase transition in interacting systems.
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Affiliation(s)
- Miroslav Hopjan
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
| | - 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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4
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Krajewski B, Vidmar L, Bonča J, Mierzejewski M. Restoring Ergodicity in a Strongly Disordered Interacting Chain. PHYSICAL REVIEW LETTERS 2022; 129:260601. [PMID: 36608198 DOI: 10.1103/physrevlett.129.260601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 12/06/2022] [Indexed: 06/17/2023]
Abstract
We consider a chain of interacting fermions with random disorder that was intensively studied in the context of many-body localization. We show that only a small fraction of the two-body interaction represents a true local perturbation to the Anderson insulator. While this true perturbation is nonzero at any finite disorder strength W, it decreases with increasing W. This establishes a view that the strongly disordered system should be viewed as a weakly perturbed integrable model, i.e., a weakly perturbed Anderson insulator. As a consequence, the latter can hardly be distinguished from a strictly integrable system in finite-size calculations at large W. We then introduce a rescaled model in which the true perturbation is of the same order of magnitude as the other terms of the Hamiltonian, and show that the system remains ergodic at arbitrary large disorder.
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Affiliation(s)
- B Krajewski
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - L 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
| | - J Bonča
- 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
| | - M Mierzejewski
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
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5
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Sels D, Polkovnikov A. Dynamical obstruction to localization in a disordered spin chain. Phys Rev E 2021; 104:054105. [PMID: 34942719 DOI: 10.1103/physreve.104.054105] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Accepted: 10/05/2021] [Indexed: 11/07/2022]
Abstract
We analyze a one-dimensional XXZ spin chain in a disordered magnetic field. As the main probes of the system's behavior, we use the sensitivity of eigenstates to adiabatic transformations, as expressed through the fidelity susceptibility, in conjunction with the low-frequency asymptotes of the spectral function. We identify a region of maximal chaos-with exponentially enhanced susceptibility-which separates the many-body localized phase from the diffusive ergodic phase. This regime is characterized by slow transport, and we argue that the presence of such slow dynamics highly constrains any possible localization transition in the thermodynamic limit. Rather, the results are more consistent with absence of the localized phase.
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Affiliation(s)
- Dries Sels
- Department of Physics, New York University, New York, New York 10003, USA.,Center for Computational Quantum Physics, Flatiron Institute, New York 10010, New York, USA
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6
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One-Dimensional Disordered Bosonic Systems. ATOMS 2021. [DOI: 10.3390/atoms9040112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system. Despite the growing interest in this topic, a complete understanding of the issue is still missing. An open question, for example, is the description of the interplay of disorder and interactions, which has been predicted to give rise to exotic states of matter such as quantum glasses or many-body localization. In this review, we will present an overview of experimental observations with disordered quantum gases, focused on one-dimensional bosons, and we will connect them with theoretical predictions.
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7
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Guo Q, Cheng C, Li H, Xu S, Zhang P, Wang Z, Song C, Liu W, Ren W, Dong H, Mondaini R, Wang H. Stark Many-Body Localization on a Superconducting Quantum Processor. PHYSICAL REVIEW LETTERS 2021; 127:240502. [PMID: 34951777 DOI: 10.1103/physrevlett.127.240502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2021] [Accepted: 11/08/2021] [Indexed: 06/14/2023]
Abstract
Quantum emulators, owing to their large degree of tunability and control, allow the observation of fine aspects of closed quantum many-body systems, as either the regime where thermalization takes place or when it is halted by the presence of disorder. The latter, dubbed many-body localization (MBL) phenomenon, describes the nonergodic behavior that is dynamically identified by the preservation of local information and slow entanglement growth. Here, we provide a precise observation of this same phenomenology in the case where the quenched on-site energy landscape is not disordered, but rather linearly varied, emulating the Stark MBL. To this end, we construct a quantum device composed of 29 functional superconducting qubits, faithfully reproducing the relaxation dynamics of a nonintegrable spin model. At large Stark potentials, local observables display periodic Bloch oscillations, a manifesting characteristic of the fragmentation of the Hilbert space in sectors that conserve dipole moments. The flexible programmability of our quantum emulator highlights its potential in helping the understanding of nontrivial quantum many-body problems, in direct complement to simulations in classical computers.
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Affiliation(s)
- Qiujiang Guo
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Chen Cheng
- School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
- Beijing Computational Science Research Center, Beijing 100094, China
| | - Hekang Li
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Shibo Xu
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Pengfei Zhang
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Zhen Wang
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Chao Song
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Wuxin Liu
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Wenhui Ren
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Hang Dong
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Rubem Mondaini
- Beijing Computational Science Research Center, Beijing 100094, China
| | - H Wang
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
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8
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Vidmar L, Krajewski B, Bonča J, Mierzejewski M. Phenomenology of Spectral Functions in Disordered Spin Chains at Infinite Temperature. PHYSICAL REVIEW LETTERS 2021; 127:230603. [PMID: 34936803 DOI: 10.1103/physrevlett.127.230603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Accepted: 11/01/2021] [Indexed: 06/14/2023]
Abstract
Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition. For the paradigmatic random field Heisenberg spin chains, many intriguing features were observed when the disorder is considerable compared to the spin interaction strength. Here, we introduce a phenomenological theory that may explain some of those features. The theory is based on the proximity to the noninteracting limit, in which the system is an Anderson insulator. Taking the spin imbalance as an exemplary observable, we demonstrate that the proximity to the local integrals of motion of the Anderson insulator determines the dynamics of the observable at infinite temperature. In finite interacting systems our theory quantitatively describes its integrated spectral function for a wide range of disorders.
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Affiliation(s)
- 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
| | - Bartosz Krajewski
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - Janez Bonča
- 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
| | - Marcin Mierzejewski
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
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9
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Sierant P, Lazo EG, Dalmonte M, Scardicchio A, Zakrzewski J. Constraint-Induced Delocalization. PHYSICAL REVIEW LETTERS 2021; 127:126603. [PMID: 34597060 DOI: 10.1103/physrevlett.127.126603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Accepted: 08/12/2021] [Indexed: 06/13/2023]
Abstract
We study the impact of quenched disorder on the dynamics of locally constrained quantum spin chains, that describe 1D arrays of Rydberg atoms in both the frozen (Ising-type) and dressed (XY-type) regime. Performing large-scale numerical experiments, we observe no trace of many-body localization even at large disorder. Analyzing the role of quenched disorder terms in constrained systems we show that they act in two, distinct and competing ways: as an on-site disorder term for the basic excitations of the system, and as an interaction between excitations. The two contributions are of the same order, and as they compete (one towards localization, the other against it), one does never enter a truly strong disorder, weak interaction limit, where many-body localization occurs. Such a mechanism is further clarified in the case of XY-type constrained models: there, a term which would represent a bona fide local quenched disorder term acting on the excitations of the clean model must be written as a series of nonlocal terms in the unconstrained variables. Our observations provide a simple picture to interpret the role of quenched disorder that could be immediately extended to other constrained models or quenched gauge theories.
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Affiliation(s)
- Piotr Sierant
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Eduardo Gonzalez Lazo
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- SISSA, via Bonomea, 265, 34136 Trieste, Italy
| | - Marcello Dalmonte
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- SISSA, via Bonomea, 265, 34136 Trieste, Italy
| | - Antonello Scardicchio
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- INFN Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy
| | - Jakub Zakrzewski
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
- Mark Kac Complex Systems Research Center, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
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10
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Martínez-Peña R, Giorgi GL, Nokkala J, Soriano MC, Zambrini R. Dynamical Phase Transitions in Quantum Reservoir Computing. PHYSICAL REVIEW LETTERS 2021; 127:100502. [PMID: 34533342 DOI: 10.1103/physrevlett.127.100502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Revised: 06/11/2021] [Accepted: 07/19/2021] [Indexed: 05/26/2023]
Abstract
Closed quantum systems exhibit different dynamical regimes, like many-body localization or thermalization, which determine the mechanisms of spread and processing of information. Here we address the impact of these dynamical phases in quantum reservoir computing, an unconventional computing paradigm recently extended into the quantum regime that exploits dynamical systems to solve nonlinear and temporal tasks. We establish that the thermal phase is naturally adapted to the requirements of quantum reservoir computing and report an increased performance at the thermalization transition for the studied tasks. Uncovering the underlying physical mechanisms behind optimal information processing capabilities of spin networks is essential for future experimental implementations and provides a new perspective on dynamical phases.
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Affiliation(s)
- Rodrigo Martínez-Peña
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Gian Luca Giorgi
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Johannes Nokkala
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Miguel C Soriano
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Roberta Zambrini
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
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11
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Chertkov E, Villalonga B, Clark BK. Numerical Evidence for Many-Body Localization in Two and Three Dimensions. PHYSICAL REVIEW LETTERS 2021; 126:180602. [PMID: 34018807 DOI: 10.1103/physrevlett.126.180602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2020] [Accepted: 04/09/2021] [Indexed: 06/12/2023]
Abstract
Disorder and interactions can lead to the breakdown of statistical mechanics in certain quantum systems, a phenomenon known as many-body localization (MBL). Much of the phenomenology of MBL emerges from the existence of ℓ bits, a set of conserved quantities that are quasilocal and binary (i.e., possess only ±1 eigenvalues). While MBL and ℓ bits are known to exist in one-dimensional systems, their existence in dimensions greater than one is a key open question. To tackle this question, we develop an algorithm that can find approximate binary ℓ bits in arbitrary dimensions by adaptively generating a basis of operators in which to represent the ℓ bit. We use the algorithm to study four models: the one-, two-, and three-dimensional disordered Heisenberg models and the two-dimensional disordered hard-core Bose-Hubbard model. For all four of the models studied, our algorithm finds high-quality ℓ bits at large disorder strength and rapid qualitative changes in the distributions of ℓ bits in particular ranges of disorder strengths, suggesting the existence of MBL transitions. These transitions in the one-dimensional Heisenberg model and two-dimensional Bose-Hubbard model coincide well with past estimates of the critical disorder strengths in these models, which further validates the evidence of MBL phenomenology in the other two- and three-dimensional models we examine. In addition to finding MBL behavior in higher dimensions, our algorithm can be used to probe MBL in various geometries and dimensionality.
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Affiliation(s)
- Eli Chertkov
- Institute for Condensed Matter Theory and IQUIST and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Benjamin Villalonga
- Institute for Condensed Matter Theory and IQUIST and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Bryan K Clark
- Institute for Condensed Matter Theory and IQUIST and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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12
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Sahay R, Machado F, Ye B, Laumann CR, Yao NY. Emergent Ergodicity at the Transition between Many-Body Localized Phases. PHYSICAL REVIEW LETTERS 2021; 126:100604. [PMID: 33784134 DOI: 10.1103/physrevlett.126.100604] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2020] [Accepted: 12/23/2020] [Indexed: 06/12/2023]
Abstract
Strongly disordered systems in the many-body localized (MBL) phase can exhibit ground state order in highly excited eigenstates. The interplay between localization, symmetry, and topology has led to the characterization of a broad landscape of MBL phases ranging from spin glasses and time crystals to symmetry protected topological phases. Understanding the nature of phase transitions between these different forms of eigenstate order remains an essential open question. Here, we conjecture that no direct transition between distinct MBL orders can occur in one dimension; rather, an ergodic phase always intervenes. Motivated by recent advances in Rydberg-atom-based quantum simulation, we propose an experimental protocol where the intervening ergodic phase can be diagnosed via the dynamics of local observables.
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Affiliation(s)
- Rahul Sahay
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Francisco Machado
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Bingtian Ye
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Chris R Laumann
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - Norman Y Yao
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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13
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Xu X, Poletti D. Localization-delocalization effects of a delocalizing dissipation on disordered XXZ spin chains. CHAOS (WOODBURY, N.Y.) 2021; 31:033133. [PMID: 33810755 DOI: 10.1063/5.0038401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2020] [Accepted: 02/23/2021] [Indexed: 06/12/2023]
Abstract
The interplay between interaction, disorder, and dissipation has shown a rich phenomenology. Here, we investigate a disordered XXZ spin chain in contact with a bath which, alone, would drive the system toward a highly delocalized and coherent Dicke state. We show that there exist regimes for which the natural orbitals of the single-particle density matrix of the steady state are all localized in the presence of strong disorders, for either weak interaction or strong interaction. We show that the averaged steady-state occupation in the eigenbasis of the open system Hamiltonian could follow an exponential decay for intermediate disorder strength in the presence of weak interactions, while it is more evenly spread for strong disorder or for stronger interactions. Last, we show that strong dissipation increases the coherence of the steady states, thus reducing the signatures of localization. We capture such signatures of localization also with a concatenated inverse participation ratio that simultaneously takes into account how localized are the eigenstates of the Hamiltonian and how close is the steady state to an incoherent mixture of different energy eigenstates.
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Affiliation(s)
- Xiansong Xu
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - Dario Poletti
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
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14
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Šuntajs J, Bonča J, Prosen T, Vidmar L. Quantum chaos challenges many-body localization. Phys Rev E 2020; 102:062144. [PMID: 33466008 DOI: 10.1103/physreve.102.062144] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2020] [Accepted: 12/02/2020] [Indexed: 06/12/2023]
Abstract
Characterizing states of matter through the lens of their ergodic properties is a fascinating new direction of research. In the quantum realm, the many-body localization (MBL) was proposed to be the paradigmatic ergodicity breaking phenomenon, which extends the concept of Anderson localization to interacting systems. At the same time, random matrix theory has established a powerful framework for characterizing the onset of quantum chaos and ergodicity (or the absence thereof) in quantum many-body systems. Here we numerically study the spectral statistics of disordered interacting spin chains, which represent prototype models expected to exhibit MBL. We study the ergodicity indicator g=log_{10}(t_{H}/t_{Th}), which is defined through the ratio of two characteristic many-body time scales, the Thouless time t_{Th} and the Heisenberg time t_{H}, and hence resembles the logarithm of the dimensionless conductance introduced in the context of Anderson localization. We argue that the ergodicity breaking transition in interacting spin chains occurs when both time scales are of the same order, t_{Th}≈t_{H}, and g becomes a system-size independent constant. Hence, the ergodicity breaking transition in many-body systems carries certain analogies with the Anderson localization transition. Intriguingly, using a Berezinskii-Kosterlitz-Thouless correlation length we observe a scaling solution of g across the transition, which allows for detection of the crossing point in finite systems. We discuss the observation that scaled results in finite systems by increasing the system size exhibit a flow towards the quantum chaotic regime.
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Affiliation(s)
- Jan Šuntajs
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
| | - Janez Bonča
- 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
| | - Tomaž Prosen
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - 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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15
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Sierant P, Lewenstein M, Zakrzewski J. Polynomially Filtered Exact Diagonalization Approach to Many-Body Localization. PHYSICAL REVIEW LETTERS 2020; 125:156601. [PMID: 33095617 DOI: 10.1103/physrevlett.125.156601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2020] [Accepted: 09/13/2020] [Indexed: 06/11/2023]
Abstract
Polynomially filtered exact diagonalization method (POLFED) for large sparse matrices is introduced. The algorithm finds an optimal basis of a subspace spanned by eigenvectors with eigenvalues close to a specified energy target by a spectral transformation using a high order polynomial of the matrix. The memory requirements scale better with system size than in the state-of-the-art shift-invert approach. The potential of POLFED is demonstrated examining many-body localization transition in 1D interacting quantum spin-1/2 chains. We investigate the disorder strength and system size scaling of Thouless time. System size dependence of bipartite entanglement entropy and of the gap ratio highlights the importance of finite-size effects. We discuss possible scenarios regarding the many-body localization transition obtaining estimates for the critical disorder strength.
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Affiliation(s)
- Piotr Sierant
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
| | - Maciej Lewenstein
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
- ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain
| | - Jakub Zakrzewski
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
- Mark Kac Complex Systems Research Center, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
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Lenarčič Z, Alberton O, Rosch A, Altman E. Critical Behavior near the Many-Body Localization Transition in Driven Open Systems. PHYSICAL REVIEW LETTERS 2020; 125:116601. [PMID: 32976013 DOI: 10.1103/physrevlett.125.116601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Accepted: 08/12/2020] [Indexed: 06/11/2023]
Abstract
Coupling a many-body localized system to a thermal bath breaks local conservation laws and washes out signatures of localization. When the bath is nonthermal or when the system is also weakly driven, local conserved quantities acquire a highly nonthermal stationary value. We demonstrate how this property can be used to study the many-body localization phase transition in weakly open systems. Here, the strength of the coupling to the nonthermal baths plays a similar role as a finite temperature in a T=0 quantum phase transition. By tuning this parameter, we can detect key features of the many-body localization (MBL) transition: the divergence of the dynamical exponent due to Griffiths effects in one dimension and the critical disorder strength. We apply these ideas to study the MBL critical point numerically. The possibility to observe critical signatures of the MBL transition in an open system allows for new numerical approaches that overcome the limitations of exact diagonalization studies. Here, we propose a scalable numerical scheme to study the MBL critical point using matrix-product operator solution to the Lindblad equation.
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Affiliation(s)
- Zala Lenarčič
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Ori Alberton
- Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
| | - Achim Rosch
- Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
| | - Ehud Altman
- Department of Physics, University of California, Berkeley, California 94720, USA
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Sierant P, Delande D, Zakrzewski J. Thouless Time Analysis of Anderson and Many-Body Localization Transitions. PHYSICAL REVIEW LETTERS 2020; 124:186601. [PMID: 32441956 DOI: 10.1103/physrevlett.124.186601] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2019] [Revised: 02/11/2020] [Accepted: 04/13/2020] [Indexed: 06/11/2023]
Abstract
Spectral statistics of disordered systems encode Thouless and Heisenberg timescales, whose ratio determines whether the system is chaotic or localized. We show that the scaling of the Thouless time with the system size and disorder strength is very similar in one-body Anderson models and in disordered quantum many-body systems. We argue that the two parameter scaling breaks down in the vicinity of the transition to the localized phase, signaling a slowing-down of dynamics.
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Affiliation(s)
- Piotr Sierant
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Dominique Delande
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 Place Jussieu, 75005 Paris, France
| | - Jakub Zakrzewski
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
- Mark Kac Complex Systems Research Center, Uniwersytet Jagielloński, 30-348 Kraków, Poland
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Wang Z, Fu W, Zhang Y, Zhao H. Wave-Turbulence Origin of the Instability of Anderson Localization against Many-Body Interactions. PHYSICAL REVIEW LETTERS 2020; 124:186401. [PMID: 32441955 DOI: 10.1103/physrevlett.124.186401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2019] [Revised: 02/08/2020] [Accepted: 04/03/2020] [Indexed: 06/11/2023]
Abstract
Whether Anderson localization is robust against many-body interactions and, closely related, whether a disordered many-body system can be thermalized are long outstanding issues. In this Letter, we address these issues with the wave-turbulence theory. We show that, in general, the thermalization time in one-dimensional disordered lattice systems is inversely proportional to the squared interaction strength in the thermodynamic limit. It leads to the conclusion that such systems can always be thermalized by arbitrarily weak many-body interactions and thus the localized states are unstable.
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Affiliation(s)
- Zhen Wang
- Department of Physics, Xiamen University, Xiamen 361005, Fujian, China
| | - Weicheng Fu
- Department of Physics, Xiamen University, Xiamen 361005, Fujian, China
| | - Yong Zhang
- Department of Physics, Xiamen University, Xiamen 361005, Fujian, China
| | - Hong Zhao
- Department of Physics, Xiamen University, Xiamen 361005, Fujian, China
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Modak R, Nag T. Many-body localization in a long-range model: Real-space renormalization-group study. Phys Rev E 2020; 101:052108. [PMID: 32575219 DOI: 10.1103/physreve.101.052108] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2019] [Accepted: 04/17/2020] [Indexed: 11/07/2022]
Abstract
We develop a real-space renormalization-group (RSRG) scheme by appropriately inserting the long-range hopping t∼r^{-α} with nearest-neighbor interaction to study the entanglement entropy and maximum block size for the many-body localization (MBL) transition. We show that for α<2 there exists a localization transition with renormalized disorder that depends logarithmically on the finite size of the system. The transition observed for α>2 does not need a rescaling in disorder strength. Most important, we find that even though the MBL transition for α>2 falls in the same universality class as that of the short-range models, the transition for α<2 belongs to a different universality class. Because of the intrinsic nature of the RSRG flow toward delocalization, MBL phase for α>2 might suffer an instability in the thermodynamic limit while the underlying systems support algebraic localization. Moreover, we verify these findings by inserting microscopic details to the RSRG scheme where we additionally find a more appropriate rescaling function for disorder strength; we indeed uncover a power-law scaling with a logarithmic correction and a distinctly different stretched exponential scaling for α<2 and α>2, respectively, by analyzing system with finite size. This finding further suggests that microscopic RSRG scheme is able to give a hint of instability of the MBL phase for α>2 even considering systems of finite size.
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Affiliation(s)
- Ranjan Modak
- SISSA and INFN, via Bonomea 265, 34136 Trieste, Italy
| | - Tanay Nag
- SISSA, via Bonomea 265, 34136 Trieste, Italy
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