Graph-theory measures capture weak ergodicity breaking on large quantum systems
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, a scenario called a weak ergodicity-breaking transition. This situation is realized in the Rosenzweig-Porter model and the quantum sun model, which we investigate here. Our analysis is based on representing quantum systems in Fock space and examining the short-time dynamics of density autocorrelation functions. From these, we extract proxies for decay rates for each individual basis state. As a first main result, we show that the distribution of such decay rates captures known weak ergodicity-breaking transitions in both models. As a second main result, we establish a connection between the decay rates of density autocorrelations and graph-theoretical measures. Concretely, we demonstrate that moments of the distribution of the recently introduced graph-energy centrality also detect the weak ergodicity transitions, which is inherited from the behavior of the decay rates. While most numerical tools are limited to small system sizes, the quantities studied in our work can be calculated analytically for large systems of many hundreds of sites and in some cases, even in the thermodynamic limit.
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BibTeX
@misc{menzler2026graphtheory,
title = {{Graph-theory measures capture weak ergodicity breaking on large quantum systems}},
author = {Heiko Georg Menzler and Rafał Świętek and Mari Carmen Bañuls and Fabian Heidrich-Meisner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.00094},
eprint = {2605.00094},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.00094},
}
RIS
TY - UNPB
TI - Graph-theory measures capture weak ergodicity breaking on large quantum systems
AU - Heiko Georg Menzler
AU - Rafał Świętek
AU - Mari Carmen Bañuls
AU - Fabian Heidrich-Meisner
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2605.00094
UR - https://arxiv.org/abs/2605.00094
AB - 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, a scenario called a weak ergodicity-breaking transition. This situation is realized in the Rosenzweig-Porter model and the quantum sun model, which we investigate here. Our analysis is based on representing quantum systems in Fock space and examining the short-time dynamics of density autocorrelation functions. From these, we extract proxies for decay rates for each individual basis state. As a first main result, we show that the distribution of such decay rates captures known weak ergodicity-breaking transitions in both models. As a second main result, we establish a connection between the decay rates of density autocorrelations and graph-theoretical measures. Concretely, we demonstrate that moments of the distribution of the recently introduced graph-energy centrality also detect the weak ergodicity transitions, which is inherited from the behavior of the decay rates. While most numerical tools are limited to small system sizes, the quantities studied in our work can be calculated analytically for large systems of many hundreds of sites and in some cases, even in the thermodynamic limit.
ER -