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.
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.
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.
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.
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.