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

We study the onset of weak ergodicity violations in closed quantum many-body systems andfocus 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-theoreticalmeasures. As a main result, we show that the recently introduced graph-energy centrality capturesknown weak ergodicity-breaking transitions via characteristic changes in its distribution. While mostnumerical tools are limited to small system sizes, our measure can be calculated analytically for largesystems of many hundreds of sites and in some cases, even in the thermodynamic limit. We concludeby demonstrating the applicability of our Fock-space based measure to a kinetically constrainedquantum model, where we find evidence for a weak ergodicity-breaking transition accompanied byglassy dynamics.