Dynamics of many-body localization in a translation-invariant quantum glass model

Horssen, Merlijn van; Levi, Emanuele; Garrahan, Juan P.

doi:10.1103/physrevb.92.100305

Cited by 157 publications

(152 citation statements)

References 65 publications

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“…Hence, these systems have been dubbed quasi-MBL [14][15][16]. Similar phenomenology has been observed in the corresponding quantum dynamics of classical glassy models [17,18]. Intriguingly, some evidence for QDL-like behaviour, showing different timescales for equilibration of two subsystems, has been observed in cold-atom experiments [19].…”

mentioning

confidence: 80%

Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Localization

Smith¹,

Knolle²,

Moessner

et al. 2017

Phys. Rev. Lett.

122

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We study the time evolution after a quantum quench in a family of models whose degrees of freedom are fermions coupled to spins, where quenched disorder appears neither in the Hamiltonian parameters nor in the initial state. Focussing on the behaviour of entanglement, both spatial and between subsystems, we show that the model supports a state exhibiting combined area/volume law entanglement, being characteristic of the quantum disentangled liquid. This behaviour appears for one set of variables, which is related via a duality mapping to another set, where this structure is absent. Upon adding density interactions between the fermions, we identify an exact mapping to an XXZ spin-chain in a random binary magnetic field, thereby establishing the existence of many-body localization with its logarithmic entanglement growth in a fully disorder-free system.The intriguing problem of the interplay between interactions and disorder in a quantum system has been fuelling research in this field since Anderson's original work [1]. Recent progress in understanding physical phenomena associated with this interplay [2-4] has firmly placed many-body localization (MBL) ideas among the central paradigms of manybody physics [5,6]. These exciting developments moved disordered interacting systems into the focus of attention, not least because MBL offers new important insights into the fundamental questions of ergodicity and its breaking, such as concepts of eigenstate thermalization hypothesis [7][8][9], beyond the realm of integrable models. Because the presence/absence of ergodicity defines the way a generic system relaxes towards an equilibrium state, there are many interesting connections between the physics of MBL, and nonequilibrium quantum physics, e.g. quantum quenches.One of such connections, recently proposed theoretically [10][11][12], suggests a new non-ergodic state of matter -the quantum disentangled liquid (QDL) -which complements the established phenomenology of relaxation in isolated manybody quantum systems. The defining feature of these quantum liquids is that they are unable to fully thermalize because of interactions, thus making unnecessary the usual requirements for ergodicity breaking, such as integrability or quenched disorder. The idea of QDLs can be traced back to early works of Kagan and Maksimov on interaction-induced localization, discussed in the context of solid Helium [13]. One QDL scenario is that of heavy particles which thermalize, while light particles evade thermalization by localizing on the heavy particles. More recent studies of heavy-light particle models suggest that this physical picture of sub-diffusive dynamics, while present, is only transient, and gives way to ergodic behaviour at long times. Hence, these systems have been dubbed quasi-MBL [14][15][16]. Similar phenomenology has been observed in the corresponding quantum dynamics of classical glassy models [17,18]. Intriguingly, some evidence for QDL-like behaviour, showing different timescales for equilibration of two subsystems, has b...

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mentioning

confidence: 80%

Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Localization

Smith¹,

Knolle²,

Moessner

et al. 2017

Phys. Rev. Lett.

122

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“…Finally, we mention some further directions opened by this study. First, we expect that this method will be useful for studying MBL and ergodicity breaking in other contexts, for example, in the translationally invariant models that were conjectured to break ergodicity [52][53][54][55][56][57][58][59]. Second, our results provide a natural starting point for developing a microscopic RG procedure for the MBL transition.…”

Section: Discussionmentioning

confidence: 99%

Criterion for Many-Body Localization-Delocalization Phase Transition

2015

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We propose a new approach to probing ergodicity and its breakdown in one-dimensional quantum manybody systems based on their response to a local perturbation. We study the distribution of matrix elements of a local operator between the system's eigenstates, finding a qualitatively different behavior in the manybody localized (MBL) and ergodic phases. To characterize how strongly a local perturbation modifies the eigenstates, we introduce the parameter GðLÞ ¼ hlnðV nm =δÞi, which represents the disorder-averaged ratio of a typical matrix element of a local operator V to energy level spacing δ; this parameter is reminiscent of the Thouless conductance in the single-particle localization. We show that the parameter GðLÞ decreases with system size L in the MBL phase and grows in the ergodic phase. We surmise that the delocalization transition occurs when GðLÞ is independent of system size, GðLÞ ¼ G c ∼ 1. We illustrate our approach by studying the many-body localization transition and resolving the many-body mobility edge in a disordered one-dimensional XXZ spin-1=2 chain using exact diagonalization and time-evolving block-decimation methods. Our criterion for the MBL transition gives insights into microscopic details of transition. Its direct physical consequences, in particular, logarithmically slow transport at the transition and extensive entanglement entropy of the eigenstates, are consistent with recent renormalization-group predictions.

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“…The operator Π k in H represents the simplest choice which effectively reproduces the requirement of an active site nearby to flip a spin; this makes H the "minimal quantum equivalent" of the noisy branching/coagulation above. Similar "constrained" Hamiltonians have been studied in the past with a focus on many-body localization [47,48].…”

Section: Modelmentioning

confidence: 99%

Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations

et al. 2016

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Stochastic processes with absorbing states feature remarkable examples of non-equilibrium universal phenomena. While a broad understanding has been progressively established in the classical regime, relatively little is known about the behavior of these non-equilibrium systems in the presence of quantum fluctuations. Here we theoretically address such a scenario in an open quantum spin model which in its classical limit undergoes a directed percolation phase transition. By mapping the problem to a non-equilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin-flips alters the nature of the transition such that it becomes first-order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states.

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Dynamics of many-body localization in a translation-invariant quantum glass model

Cited by 157 publications

References 65 publications

Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Localization

Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Localization

Criterion for Many-Body Localization-Delocalization Phase Transition

Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations

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