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arXiv:2402.01362 · Physical review. B./Physical review. B

Catching thermal avalanches in the disordered XXZ model

Tomasz Szołdra, Piotr Sierant, Maciej Lewenstein, Jakub Zakrzewski

Published Apr 8, 2024• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.109.134202

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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.
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.
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Quantum avalanches in Z2\mathbb {Z}_2Z2​-preserving interacting Ising Majorana chain
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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.
We propose a multiscale diagonalization scheme to study disordered one-dimensional chains, in particular, the transition between many-body localization (MBL) and the ergodic phase, expected to be governed by resonant spots. Our scheme focuses on the dichotomy of MBL versus validity of the eigenstate thermalization hypothesis. We show that a few natural assumptions imply that the system is localized with probability one at criticality. On the ergodic side, delocalization is induced by a quantum avalanche seeded by large ergodic spots, whose size diverges at the transition. On the MBL side, the typical localization length tends to the inverse of the maximal entropy density at the transition, but there is a divergent length scale related to the response to an inclusion of large ergodic spots. A mean-field approximation analytically illustrates these results and predicts a power-law distribution for thermal inclusions at criticality.
We investigate the effect of ergodic inclusions in putative many-body localized systems. To this end, we consider the random field Heisenberg chain, which is many-body localized at strong disorder and we couple it to an ergodic bubble, modeled by a random matrix Hamiltonian. Recent theoretical work suggests that the ergodic bubble destabilizes the apparent localized phase at intermediate disorder strength and finite sizes. We tentatively confirm this by numerically analyzing the response of the local thermality, quantified by one-site purities, to the insertion of the bubble. For a range of intermediate disorder strengths, this response decays very slowly, or not at all, with increasing distance to the bubble. This suggests that at those disorder strengths, the system is delocalized in the thermodynamic limit. However, the numerics is unfortunately not unambiguous and we cannot definitely rule out artefacts.