Graph-theory measures capture weak ergodicity breaking on large quantum systems

TL;DR

This paper introduces a graph-theoretical measure based on Fock space representations to detect weak ergodicity-breaking transitions in large quantum many-body systems, including analytical calculations for large systems.

Contribution

It demonstrates that graph-energy centrality effectively captures ergodicity-breaking transitions and can be computed analytically for large systems, surpassing traditional numerical limitations.

Findings

Graph-energy centrality signals known ergodicity-breaking transitions.

The measure is analytically calculable for systems with hundreds of sites.

Application to a kinetically constrained model shows evidence of glassy dynamics.

Abstract

We study the onset of weak ergodicity violations in closed quantum many-body systems and focus on cases in which they occur through a transition that is controlled by a model parameter. Our analysis is based on representing quantum systems in Fock space and utilizes graph-theoretical measures. As a main result, we show that the recently introduced graph-energy centrality captures known weak ergodicity-breaking transitions via characteristic changes in its distribution. While most numerical tools are limited to small system sizes, our measure can be calculated analytically for large systems of many hundreds of sites and in some cases, even in the thermodynamic limit. We conclude by demonstrating the applicability of our Fock-space based measure to a kinetically constrained quantum model, where we find evidence for a weak ergodicity-breaking transition accompanied by glassy dynamics.