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arXiv:2107.05642 · Physical review. B./Physical review. B

Avalanches and many-body resonances in many-body localized systems

Alan Morningstar, Luis Colmenárez, Vedika Khemani, David J. Luitz, David A. Huse

Published May 12, 2022• 257 citations
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Abstract

Many-body localization (MBL) is a mechanism by which quantum chains with strong enough disorder can avoid thermalization. Here, the authors define and locate several distinct landmarks having to do with thermalization, rare many-body resonances, and so-called thermal avalanches in systems that can exhibit MBL. These landmarks are well separated in the strength of the disorder, and the estimate of where MBL breaks down in asymptotically large systems is far beyond what is usually pointed to as the MBL transition.

DOI
10.1103/physrevb.105.174205

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Many-body localization (MBL) is a mechanism by which quantum chains with strong enough disorder can avoid thermalization. Here, the authors define and locate several distinct landmarks having to do with thermalization, rare many-body resonances, and so-called thermal avalanches in systems that can exhibit MBL. These landmarks are well separated in the strength of the disorder, and the estimate of where MBL breaks down in asymptotically large systems is far beyond what is usually pointed to as the MBL transition.
Many-body localized (MBL) systems fail to reach thermal equilibrium under their own dynamics, even though they are interacting, nonintegrable, and in an extensively excited state. One instability toward thermalization of MBL systems is the so-called "avalanche," where a locally thermalizing rare region is able to spread thermalization through the full system. The spreading of the avalanche may be modeled and numerically studied in finite one-dimensional MBL systems by weakly coupling an infinite-temperature bath to one end of the system. We find that the avalanche spreads primarily via strong many-body resonances between rare near-resonant eigenstates of the closed system. Thus we find and explore a detailed connection between many-body resonances and avalanches in MBL systems.
The nature of the many-body localization (MBL) transition and even the existence of the MBL phase in random many-body quantum systems have been actively debated in recent years. In spatial dimension d>1d>1d>1, there is some consensus that the MBL phase is unstable to rare thermal inclusions that can lead to an avalanche that thermalizes the whole system. In this note, we explore the possibility of MBL in quasiperiodic systems in dimension d>1d>1d>1. We argue that (i) the MBL phase is stable against ``avalanches'' at strong enough quasiperiodic modulations for d=2d=2d=2, and (ii) the possibility of an avalanche strongly constrains the finite-size scaling behavior of the MBL transition. We present a suggestive construction that MBL is unstable for $d\ensuremath{\ge}3$.
Disordered quantum many-body systems pose one of the central challenges in condensed matter physics and quantum information science, as their dynamics are generally intractable for classical computation. Many-body localization (MBL), hypothesized to evade thermalization indefinitely under strong disorder, exemplifies this difficulty. Here, we study the stability of MBL in two dimensions using ultracold atoms in optical lattices with variable system sizes up to 24×2424\times 2424×24 sites, well beyond the classically simulable regime. Using the imbalance as a probe, we trace the long-time dynamics under two distinctive disorder potentials: quasiperiodic and random disorder. For random disorder, the MBL crossover point shifts to higher disorder strength with increasing system size, consistent with the avalanche scenario. In contrast, with quasiperiodic disorder, we observe no clear system size dependence, suggesting possible stability of MBL in two dimensions.
Disorder and interactions can lead to the breakdown of statistical mechanics in quantum systems by transitioning to a many-body localized (MBL) phase. The thermal-to-MBL transition occurs by either increasing the amount of disorder present in a system or by decreasing its energy until it crosses the so-called mobility edge. The authors construct a set of approximate integrals of motion that are quasi-universal across the energy spectrum and, thus, across the mobility edge, too. Interestingly, MBL eigenstates under the mobility edge are aware of the existence of a thermal phase at a higher energy. The phase diagram is probed close to the transition and in the MBL phase. One finds a universal distribution of the strength of the couplings of the integrals of motion in the strong disorder limit.
Strong disorder in many-body quantum systems leads to many-body localization (MBL), manifested as long-time memory of the initial state. Spatial regions of anomalously weak disorder, arising due to fluctuations in the disordered potential, may act as ergodic inclusions that seed quantum avalanches and destabilize the MBL. To investigate this mechanism in a controlled setting, the authors plant ergodic inclusions by engineering regions of a weak disorder and compare the system's time evolution with predictions of the avalanche theory.