Probing the ergodicity breaking transition via violations of random matrix theoretic predictions for local observables

TL;DR

This paper investigates how local measurements can detect ergodicity breaking in quantum many-body systems by comparing observed dynamics with random matrix theory predictions, focusing on transitions like MBL, integrability, and QMBS.

Contribution

It introduces local observable-based methods to identify ergodicity breaking, using RMT predictions as benchmarks across different non-ergodic regimes.

Findings

RMT predictions are violated during ergodicity breaking transitions.

Local observables can serve as witnesses for non-ergodic behaviour.

The approach applies to MBL, integrability, and QMBS mechanisms.

Abstract

Quantum many-body systems can exhibit distinct regimes where dynamics is either ergodic, dynamically exploring an extensive region of available state-space, or non-ergodic, where the dynamics may be restricted. An example is the many-body localization (MBL) transition, where disorder induces non-ergodic behaviour. Most measures of ergodicity notably rely on global quantities, such as level spacing statistics. We explore the ability for a subsystem to probe the ergodicity of dynamics via measurement of local observables, and use expected results from random matrix theory (RMT) as a benchmark for the ergodic regime. We exploit two predictions from RMT as ergodicity is broken: the time evolution of the quantum Fisher information, and a fluctuation-dissipation relation. These are investigated in three different ergodicity breaking mechanisms, namely, as a consequence of transition to integrability, MBL, and Quantum Many-Body Scars (QMBS). We show that the predicted behaviour from RMT can be used as a potential witness for transition to non-ergodic behaviour from the measurement of local observables alone.