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 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∞ 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 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−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≈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] (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, 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.
Quantum avalanches in Z2-preserving interacting Ising Majorana chain
Recent numerical works have revealed the instability of many-body localized (MBL) phase in disordered quantum many-body systems with finite system sizes and over finite timescales. This instability originates from the rare Griffiths regions in the thermodynamic limit, which rapidly thermalize and induce an avalanche mechanism that destabilizes surrounding MBL regions. Here, we consider the [Formula: see text]-preserving interacting Ising Majorana chain, whose phase diagram is enriched by the presence of an intermediate ergodic phase separating two distinct MBL phases characterized by different long-range orders. We investigate the dynamic characteristics of the model when coupled to an infinite bath under perturbation, and through the scaling behavior of the slowest thermalization rate, we find how the critical disorder strength in finite-size systems is affected by the avalanche mechanism. We also implement the embedded inclusion model and use the time evolution of mutual information between each spin and the artificial Griffiths region to probe the diffusion of the thermal bubble. We observe that in finite-sized systems, the critical disorder strength gradually drifts away from the center. Our results show that both the MBL paramagnetic phase and MBL spin-glass phase are unstable at finite sizes.
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.
Abstract Avalanches are believed to be the mechanism behind the transition from many-body localization to the thermal phase. We utilize spin chains with constraints to study the physics of quantum avalanches by exact diagonalization of disordered systems coupled to a thermal bath. Single-spin observables are used to characterize localization and quantify the influence of the thermal bath on disordered spin chains. Constraints on the Hilbert space confine the dynamics to a subspace, effectively reducing the Hilbert space dimension and enabling the study of larger systems with limited computational resources. We study the PXP model, and in addition, we construct spin chains with constraints by searching for constraints with a genetic algorithm to reach larger system sizes. We define quantities to measure the strength of avalanches and use these to compare different models. We find that avalanches are more pronounced in models with constraints compared to those without constraints. Results from exact diagonalization are compared with those from studying the Lindblad master equation. We also identify models that exhibit no thermal phases and find stable ergodicity breaking.
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.
Abstract Understanding under which conditions physical systems thermalize is a long-standing question in many-body physics. While generic quantum systems thermalize, there are known instances where thermalization is hindered, for example in many-body localized (MBL) systems. Here we introduce a class of stochastic collision models coupling a many-body system out of thermal equilibrium to an external heat bath. We derive upper and lower bounds on the size of the bath required to thermalize the system via such models, under certain assumptions on the Hamiltonian. We use these bounds, expressed in terms of the max-relative entropy, to characterize the robustness of MBL systems against externally-induced thermalization. Our bounds are derived within the framework of resource theories using the convex split lemma, a recent tool developed in quantum information. We apply our results to the disordered Heisenberg chain, and numerically study the robustness of its MBL phase in terms of the required bath size.