Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1608.01815 · Physical review. B./Physical review. B

Stability and instability towards delocalization in many-body localization systems

Wojciech De Roeck, François Huveneers

Published Apr 18, 2017• 393 citations
arXivHTMLPDF

Abstract

Many-body localization plays an increasing role in condensed matter theory, both because it challenges the fundaments of statistical physics, and because it allows us to engineer several new, exotic, stable phases of matter. In this paper, the authors address the issue of the stability of a many-body localized material in contact with an ergodic grain, i.e., an imperfect bath made of a few interacting degrees of freedom. Thanks to detailed microscopic analysis and numerics, they conclude that such an ergodic grain eventually destabilizes the localized phase in the following cases: if the spatial dimension is higher than one, or if the spatial dimension is one but the localization length of the localized material is larger than a fixed threshold value. In realistic materials, these ergodic grains are always present as Griffiths regions where the disorder is anomalously small, and hence, the authors conclude that the localized phase in such materials is unstable, strictly speaking. Transport and thermalization are however exponentially suppressed in the distance between ergodic grains.

DOI
10.1103/physrevb.95.155129

Related papers

How a Small Quantum Bath Can Thermalize Long Localized Chains

David J. Luitz, François Huveneers, Wojciech De Roeck

We investigate the stability of the many-body localized phase for a system in contact with a single ergodic grain modeling a Griffiths region with low disorder. Our numerical analysis provides evidence that even a small ergodic grain consisting of only three qubits can delocalize a localized chain as soon as the localization length exceeds a critical value separating localized and extended regimes of the whole system. We present a simple theory, consistent with De Roeck and Huveneers's arguments in [Phys. Rev. B 95, 155129 (2017)PRBMDO2469-995010.1103/PhysRevB.95.155129] that assumes a system to be locally ergodic unless the local relaxation time determined by Fermi's golden rule is larger than the inverse level spacing. This theory predicts a critical value for the localization length that is perfectly consistent with our numerical calculations. We analyze in detail the behavior of local operators inside and outside the ergodic grain and find excellent agreement of numerics and theory.

arXiv:1705.10807•Physical Review Letters•Oct 11, 2017•181 citations

Many-Body Delocalization in the Presence of a Quantum Bath

Rubio Abadal, A., Choi, J., Zeiher, J. +4 more

Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL). Numerous studies support the stability of the MBL phase in strongly disordered one-dimensional systems. However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions. Here we address this question experimentally using a large-scale quantum simulator of ultracold bosons in a two-dimensional optical lattice. We prepare two-component mixtures of varying relative population and implement a disorder potential which is only experienced by one of the components. The second non-disordered ''clean'' component plays the role of a bath of adjustable size that is collisionally coupled to the ''dirty'' component. Our experiments show how the dynamics of the dirty component, which, when on its own, show strong evidence of localization, become affected by the coupling to the clean component. For a high clean population, the clean component appears to behave as an effective bath for the system which leads to its delocalization, while for a smaller clean population, the ability of the bath to destabilize the system becomes strongly reduced. Our results reveal how a finite-sized quantum system can bring another one towards thermalization, in a regime of complex interplay between disorder, tunneling and intercomponent interactions. They provide a new benchmark for effective theories aiming to capture the complex physics of MBL in the weakly localized regime.

•Oct 18, 2019•99 citations

Exploration of the stability of many-body localized systems in the presence of a small bath

M. Goihl, Jens Eisert, Christian Krumnow

When pushed out of equilibrium, generic interacting quantum systems equilibrate locally and are expected to evolve towards a locally thermal description despite their unitary time evolution. Systems in which disorder competes with interactions and transport can violate this expectation by exhibiting many-body localization. The strength of the disorder with respect to the other two parameters drives a transition from a thermalizing system towards a nonthermalizing one. The existence of this transition is well established both in experimental and numerical studies for finite systems. However, the stability of many-body localization in the thermodynamic limit is largely unclear. With increasing system size, a generic disordered system will contain with high probability areas of low disorder variation. If large and frequent enough, those areas constitute ergodic grains which can hybridize and thus compete with localization. While the details of this process are not yet settled, it is conceivable that if such regions appear sufficiently often, they might be powerful enough to restore thermalization. We set out to shed light on this problem by constructing potential landscapes with low disorder regions and numerically investigating their localization behavior in the Heisenberg model. Our findings suggest that many-body localization may be more stable than anticipated in other recent theoretical works.

arXiv:1902.04371•Physical review. B./Physical review. B•May 24, 2019•48 citations

Many-Body Delocalization in the Presence of a Quantum Bath

Antonio Rubio-Abadal, Jae-yoon Choi, Johannes Zeiher +4 more

Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL).Numerous studies support the stability of the MBL phase in strongly disordered one-dimensional systems.However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions.Here we address this question experimentally using a largescale quantum simulator of ultracold bosons in a two-dimensional optical lattice.We prepare two-component mixtures of varying relative population and implement a disorder potential which is experienced only by one of the components.The second nondisordered "clean" component plays the role of a bath of adjustable size that is collisionally coupled to the "dirty" component.Our experiments show how the dynamics of the dirty component, which, when on its own, show strong evidence of localization, become affected by the coupling to the clean component.For a high clean population, the clean component appears to behave as an effective bath for the system which leads to its delocalization, while for a smaller clean population, the ability of the bath to destabilize the system becomes strongly reduced.Our results reveal how a finite-sized quantum system can bring another one towards thermalization, in a regime of complex interplay between disorder, tunneling, and intercomponent interactions.They provide a new benchmark for effective theories aiming to capture the complex physics of MBL in the weakly localized regime.

arXiv:1805.00056•Physical Review X•Oct 18, 2019•95 citations

Probing many-body localization in the presence of a quantum bath

Antonio Rubio-Abadal, Jae-yoon Choi, Johannes Zeiher +4 more

Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL). Numerous studies have left no doubt about the stability of the MBL phase in strongly disordered one-dimensional systems. However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions. Here we address this question experimentally using a large-scale quantum simulator of ultracold bosons in a two-dimensional optical lattice. We prepare two-component mixtures of varying relative population and implement a disorder potential which is only experienced by one of the components. The second non-disordered clean component plays the role of a small quantum bath of adjustable size that is collisionally coupled to the dirty component. Our experiments provide evidence that MBL is remarkably stable in 2D and can even survive in the presence of a small bath for our observed long timescales. A too large bath, however, ultimately leads to the destruction of MBL.

•Apr 30, 2018•9 citations

Many-body localization in the presence of a small bath

Katharine Hyatt, James R. Garrison, Andrew C. Potter +1 more

In the presence of strong disorder and weak interactions, closed quantum systems can enter a many-body localized phase wherein the system does not conduct heat or charge, does not equilibrate even for arbitrarily long times, and robustly violates quantum statistical mechanics. While this is well established in closed quantum systems, the interplay of such systems with delocalized degrees of freedom is much less understood. Here, the authors consider a model for which, in the noninteracting limit, some degrees of freedom are localized while others remain delocalized. Such a system can be viewed as a model for a many-body localized system brought into contact with a small bath of a comparable number of degrees of freedom. The authors numerically and analytically study the effect of interactions on this system and find that in certain parameter regimes, results are consistent with interaction-induced localization of the entire system.

arXiv:1601.07184•Physical review. B./Physical review. B•Jan 19, 2017•61 citations
Many-body localization plays an increasing role in condensed matter theory, both because it challenges the fundaments of statistical physics, and because it allows us to engineer several new, exotic, stable phases of matter. In this paper, the authors address the issue of the stability of a many-body localized material in contact with an ergodic grain, i.e., an imperfect bath made of a few interacting degrees of freedom. Thanks to detailed microscopic analysis and numerics, they conclude that such an ergodic grain eventually destabilizes the localized phase in the following cases: if the spatial dimension is higher than one, or if the spatial dimension is one but the localization length of the localized material is larger than a fixed threshold value. In realistic materials, these ergodic grains are always present as Griffiths regions where the disorder is anomalously small, and hence, the authors conclude that the localized phase in such materials is unstable, strictly speaking. Transport and thermalization are however exponentially suppressed in the distance between ergodic grains.
We investigate the stability of the many-body localized phase for a system in contact with a single ergodic grain modeling a Griffiths region with low disorder. Our numerical analysis provides evidence that even a small ergodic grain consisting of only three qubits can delocalize a localized chain as soon as the localization length exceeds a critical value separating localized and extended regimes of the whole system. We present a simple theory, consistent with De Roeck and Huveneers's arguments in [Phys. Rev. B 95, 155129 (2017)PRBMDO2469-995010.1103/PhysRevB.95.155129] that assumes a system to be locally ergodic unless the local relaxation time determined by Fermi's golden rule is larger than the inverse level spacing. This theory predicts a critical value for the localization length that is perfectly consistent with our numerical calculations. We analyze in detail the behavior of local operators inside and outside the ergodic grain and find excellent agreement of numerics and theory.
Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL). Numerous studies support the stability of the MBL phase in strongly disordered one-dimensional systems. However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions. Here we address this question experimentally using a large-scale quantum simulator of ultracold bosons in a two-dimensional optical lattice. We prepare two-component mixtures of varying relative population and implement a disorder potential which is only experienced by one of the components. The second non-disordered ''clean'' component plays the role of a bath of adjustable size that is collisionally coupled to the ''dirty'' component. Our experiments show how the dynamics of the dirty component, which, when on its own, show strong evidence of localization, become affected by the coupling to the clean component. For a high clean population, the clean component appears to behave as an effective bath for the system which leads to its delocalization, while for a smaller clean population, the ability of the bath to destabilize the system becomes strongly reduced. Our results reveal how a finite-sized quantum system can bring another one towards thermalization, in a regime of complex interplay between disorder, tunneling and intercomponent interactions. They provide a new benchmark for effective theories aiming to capture the complex physics of MBL in the weakly localized regime.
When pushed out of equilibrium, generic interacting quantum systems equilibrate locally and are expected to evolve towards a locally thermal description despite their unitary time evolution. Systems in which disorder competes with interactions and transport can violate this expectation by exhibiting many-body localization. The strength of the disorder with respect to the other two parameters drives a transition from a thermalizing system towards a nonthermalizing one. The existence of this transition is well established both in experimental and numerical studies for finite systems. However, the stability of many-body localization in the thermodynamic limit is largely unclear. With increasing system size, a generic disordered system will contain with high probability areas of low disorder variation. If large and frequent enough, those areas constitute ergodic grains which can hybridize and thus compete with localization. While the details of this process are not yet settled, it is conceivable that if such regions appear sufficiently often, they might be powerful enough to restore thermalization. We set out to shed light on this problem by constructing potential landscapes with low disorder regions and numerically investigating their localization behavior in the Heisenberg model. Our findings suggest that many-body localization may be more stable than anticipated in other recent theoretical works.
Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL).Numerous studies support the stability of the MBL phase in strongly disordered one-dimensional systems.However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions.Here we address this question experimentally using a largescale quantum simulator of ultracold bosons in a two-dimensional optical lattice.We prepare two-component mixtures of varying relative population and implement a disorder potential which is experienced only by one of the components.The second nondisordered "clean" component plays the role of a bath of adjustable size that is collisionally coupled to the "dirty" component.Our experiments show how the dynamics of the dirty component, which, when on its own, show strong evidence of localization, become affected by the coupling to the clean component.For a high clean population, the clean component appears to behave as an effective bath for the system which leads to its delocalization, while for a smaller clean population, the ability of the bath to destabilize the system becomes strongly reduced.Our results reveal how a finite-sized quantum system can bring another one towards thermalization, in a regime of complex interplay between disorder, tunneling, and intercomponent interactions.They provide a new benchmark for effective theories aiming to capture the complex physics of MBL in the weakly localized regime.
Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL). Numerous studies have left no doubt about the stability of the MBL phase in strongly disordered one-dimensional systems. However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions. Here we address this question experimentally using a large-scale quantum simulator of ultracold bosons in a two-dimensional optical lattice. We prepare two-component mixtures of varying relative population and implement a disorder potential which is only experienced by one of the components. The second non-disordered clean component plays the role of a small quantum bath of adjustable size that is collisionally coupled to the dirty component. Our experiments provide evidence that MBL is remarkably stable in 2D and can even survive in the presence of a small bath for our observed long timescales. A too large bath, however, ultimately leads to the destruction of MBL.
In the presence of strong disorder and weak interactions, closed quantum systems can enter a many-body localized phase wherein the system does not conduct heat or charge, does not equilibrate even for arbitrarily long times, and robustly violates quantum statistical mechanics. While this is well established in closed quantum systems, the interplay of such systems with delocalized degrees of freedom is much less understood. Here, the authors consider a model for which, in the noninteracting limit, some degrees of freedom are localized while others remain delocalized. Such a system can be viewed as a model for a many-body localized system brought into contact with a small bath of a comparable number of degrees of freedom. The authors numerically and analytically study the effect of interactions on this system and find that in certain parameter regimes, results are consistent with interaction-induced localization of the entire system.