Exact Diagonalization Study on Avalanches in Many-Body Localized Constrained Spin Chains

Avalanche is 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 long disordered spin chains. In addition to the PXP model, we construct models by searching for constraints with a genetic algorithm to reach longer system sizes. We define quantities to measure the strength of avalanches and use these to compare different models. Avalanches are more pronounced in models with constraints compared to those without constraints. Exact diagonalization results are compared with other studies using the master equation. We also identify models that exhibit no thermal phases and find stable ergodicity breaking.