Weak ergodicity breaking transition in randomly constrained model

TL;DR

This paper studies a transition in randomly constrained models that affects the longevity of special states, revealing a phase change between thermal and weakly non-ergodic behavior with implications for Hilbert space localization.

Contribution

It introduces a tunable constrained random system exhibiting a transition between ergodic and weakly non-ergodic phases, highlighting the fragility of long-lived states in such models.

Findings

Identifies a phase transition controlled by the range parameter μ.

Shows long-lived states are fragile to perturbations.

Demonstrates partial Hilbert space exploration indicates localization.

Abstract

Experiments in Rydberg atoms have recently found unusually slow decay from a small number of special initial states. We investigate the robustness of such long-lived states (LLS) by studying an ensemble of locally constrained random systems with tunable range $\mu$. Upon varying $\mu$, we find a transition between a thermal and a weakly non-ergodic (supporting a finite number of LLS) phases. Furthermore, we demonstrate that the LLS observed in the experiments disappear upon the addition of small perturbations so that the transition reported here is distinct from known ones. We then show that the LLS dynamics explores only part of the accessible Hilbert space, thus corresponding to localisation in Hilbert space.