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arXiv:2301.04658 · Physical Review Letters

Many-Body Resonances in the Avalanche Instability of Many-Body Localization

Hyunsoo Ha, Alan Morningstar, David A. Huse

Published Jun 23, 2023• 32 citations
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Abstract

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.

DOI
10.1103/physrevlett.130.250405

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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.
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.
Coupling a one-dimensional quasiperiodic interacting system to a Markovian bath, we study the avalanche instability of the many-body localized phase numerically, finding that many-body localization (MBL) is more stable in pseudorandom quasiperiodic systems than the corresponding randomly disordered systems for a disorder strength W>8W>8W>8, potentially up to arbitrarily large system sizes. We support our conclusion by additionally developing real-space RG arguments, and we provide a detailed comparison between quasiperiodic and random MBL from the avalanche instability perspective, concluding that the two belong to different universality classes.
Many-body localization provides a mechanism to avoid thermalization in isolated interacting quantum systems. The breakdown of thermalization may be complete, when all eigenstates in the many-body spectrum become localized, or partial, when the so-called many-body mobility edge separates localized and delocalized parts of the spectrum. Previously, De Roeck et al. [arXiv:1506.01505] suggested a possible instability of the many-body mobility edge in energy density. The local ergodic regions - so called - resonantly spread throughout the system, leading to delocalization. In order to study such instability mechanism, in this work we design a model featuring many-body mobility edge in particle density: the states at small particle density are localized, while increasing the density of particles leads to delocalization. Using numerical simulations with matrix product states we demonstrate the stability of MBL with respect to small bubbles in large dilute systems for experimentally relevant timescales. In addition, we demonstrate that processes where the bubble spreads are favored over processes that lead to resonant tunneling, suggesting a possible mechanism behind the observed stability of many-body mobility edge. We conclude by proposing experiments to probe particle density mobility edge in Bose-Hubbard model.
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 $d\ensuremath{\ge}3$.
We investigate the stability of the many-body localized phase against quantum avalanche instabilities in a one-dimensional Heisenberg spin chain with long-range power-law interactions (V∝r−αV\propto r^{-α}V∝r−α). By combining exact diagonalization of static properties with Lindblad master equation simulations of open-system dynamics, we systematically map the interplay between interaction range and disorder strength. Our finite-size scaling analysis of entanglement entropy identifies a critical interaction exponent αc≈2α_c \approx 2αc​≈2, which separates a fragile regime, characterized by an exponentially diverging critical disorder, from a robust short-range regime. To rigorously test the system's resistance to avalanches, we couple the boundary to an infinite-temperature bath and track the propagation of the thermalization front into the localized bulk. We find that the characteristic thermalization time follows a unified scaling law, Trth∼exp⁡[κ(α)LW]T_{r_{\text{th}}} \sim \exp[κ(α) LW]Trth​​∼exp[κ(α)LW] (herein, LLL is the system size, and WWW is the disorder intensity), which diverges exponentially with the product of system size and disorder strength. This suppression enables the derivation of a quantitative stability criterion, Wstab(α)W_{\text{stab}}(α)Wstab​(α), representing the minimum critical disorder strength required to maintain avalanche stability. Our results confirm that the MBL phase remains asymptotically stable in the thermodynamic limit when disorder exceeds an interaction-dependent threshold, bridging theoretical debates on long-range MBL and providing a roadmap for observing these dynamics in experimental platforms such as Rydberg atom arrays.
Many-body localization is a profound phase of matter affecting the entire spectrum which emer ges in the presence of disorder in interacting many-body systems. Recently, the stability of many-body localization has been challenged by the avalanche mechanism, in which a small thermal region can spread, destabilizing localization and leading to global thermalization of the system. A key unresolved question is the critical competition between the thermal region's influence and the disorder strength required to trigger such an avalanche. Here, we numerically investigate many-body localization stability in an isolated Heisenberg spin chain of size LLL subjected to a disordered magnetic field. By embedding a tunable thermal region of size PPP, we analyze the system's behavior in both static and dynamical regimes using entanglement entropy and the gap ratio. Our study yields two main findings. Firstly, for strong disorder, the avalanche only occurs if the thermal region scales with system size, specifically when P/LP/LP/L exceeds a threshold value. Secondly, at strong disorder, we identify an intermediate phase between many-body localization and ergodic behavior as PPP increases. This intermediate phase leaves its fingerprint in both static and dynamic properties of the system and tends to vanish in the thermodynamic limit. Although our simulations are restricted to finite system sizes, the analysis suggests that these results hold in the thermodynamic limit for isolated many-body systems.