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arXiv:2607.21708

Thermal avalanches in a quasiperiodic XXZ model

Paolo Molignini, Antonio Štrkalj

Published Jul 23, 2026• 0 citations

Abstract

We study bath-induced thermalization in the many-body localized XXZ spin chain subjected to a quasiperiodic magnetic field. We engineer a thermal inclusion by setting the field strength in one part of the chain below the localization threshold and analyze thermalization via the avalanche mechanism. To study the nature of such avalanches, we use two complementary observables, namely the two-point connected correlation function and the particle-number entropy. Surprisingly, the correlations alone show no signatures of avalanches. Instead, they display a logarithmic growth of the correlation length throughout the dynamics and predict localization lengths of the local integrals of motion that remain well below the avalanche threshold. In contrast, the particle number entropy shows clear signatures of the thermal avalanche, with the avalanche front progressively propagating deeper into the localized subsystem for sufficiently large baths. The discrepancy between the two observables shows that two-point correlations are unreliable in identifying thermal avalanches in quasiperiodic systems, as opposed to the random case. On one hand, qualitative results are consistent with the analytical predictions of the standard avalanche theory. On the other hand, significant quantitative deviations persist, which could be due to short-range resonances generated by the quasiperiodic potential. Our results suggest that the standard avalanche framework requires revision to account for the short-range correlations of quasiperiodic potentials.

DOI: 10.48550/arxiv.2607.21708

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We study bath-induced thermalization in the many-body localized XXZ spin chain subjected to a quasiperiodic magnetic field. We engineer a thermal inclusion by setting the field strength in one part of the chain below the localization threshold and analyze thermalization via the avalanche mechanism. To study the nature of such avalanches, we use two complementary observables, namely the two-point connected correlation function and the particle-number entropy. Surprisingly, the correlations alone show no signatures of avalanches. Instead, they display a logarithmic growth of the correlation length throughout the dynamics and predict localization lengths of the local integrals of motion that remain well below the avalanche threshold. In contrast, the particle number entropy shows clear signatures of the thermal avalanche, with the avalanche front progressively propagating deeper into the localized subsystem for sufficiently large baths. The discrepancy between the two observables shows that two-point correlations are unreliable in identifying thermal avalanches in quasiperiodic systems, as opposed to the random case. On one hand, qualitative results are consistent with the analytical predictions of the standard avalanche theory. On the other hand, significant quantitative deviations persist, which could be due to short-range resonances generated by the quasiperiodic potential. Our results suggest that the standard avalanche framework requires revision to account for the short-range correlations of quasiperiodic potentials.

We investigate the robustness of the many-body localized (MBL) phase to the quantum-avalanche instability by studying the dynamics of a localized spin chain coupled to a $T=\ensuremath{\infty}$ thermal bath through its leftmost site. By analyzing local magnetizations we estimate the size of the thermalized sector of the chain and find that it increases logarithmically slowly in time. This logarithmically slow propagation of the thermalization front allows us to lower-bound the slowest thermalization time, and find a broad parameter range where it scales fast enough with the system size that MBL is robust against thermalization induced by avalanches. The further finding that the imbalance---a global quantity measuring localization---thermalizes over a timescale that is exponential both in disorder strength and system size is in agreement with these results.

We show that localization in quasiperiodically modulated, two-dimensional systems is stable to the presence of a finite density of ergodic grains. This contrasts with the case of randomly modulated systems, where such grains seed thermalizing avalanches. These results are obtained within a quantitatively accurate, self-consistent entanglement mean-field theory, which analytically describes two level systems connected to a central ergodic grain. The theory predicts the distribution of entanglement entropies of each two level system across eigenstates, and the late time values of dynamical observables. In addition to recovering the known phenomenology of avalanches, the theory reproduces exact diagonalization data, and predicts the spatial profile of the thermalized region when the avalanche fails.

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

L

subjected to a disordered magnetic field. By embedding a tunable thermal region of size

P

, 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/L

exceeds a threshold value. Secondly, at strong disorder, we identify an intermediate phase between many-body localization and ergodic behavior as

P

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.

Over a decade of work has culminated in the consensus that one-dimensional systems, subject to sufficiently large disorder, fail to thermalize and possess an extensive set of local integrals of motion. In this Letter, I will provide numerical evidence for the contrary. In particular, this work studies the dynamics of disordered spin chains which are weakly coupled to a Markovian bath. Within this approach, the critical disorder for stability to quantum avalanches exceeds ${W}^{*}\ensuremath{\gtrsim}20$ in the random field Heisenberg chain. In stark contrast to the Anderson insulator, the avalanche threshold drifts considerably with system size, with no evidence of saturation in the studied regime.

We numerically study quantum avalanches in one-dimensional disordered spin systems by attaching two XXZ spin chains. One chain has low disorder representing a rare Griffith's region, or thermal inclusion, and the second has larger disorder, i.e., disorder larger than the observed finite-size crossover. Comparing dynamics of this system to identical systems with uniformly large disorder, we find evidence for exponentially slow thermalization (in disorder) within the many-body localized regime when the rare region is present. We observe a decay of the spin imbalance in the bulk of the large disorder region that persists to long times $(\ensuremath{\sim}{10}^{4})$ and find a universal behavior of the spectral function.

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\propto 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

α_c \approx 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,

T_{r_{\text{th}}} \sim \exp[κ(α) LW]

(herein,

L

is the system size, and

W

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,

W_{\text{stab}}(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.