Modelling equilibration of local many-body quantum systems by random graph ensembles

TL;DR

This paper introduces structured random matrix ensembles to model local many-body quantum systems, revealing that complex matrix structures are necessary to accurately predict equilibration times, with network theory tools providing efficient proxies.

Contribution

The paper develops structured random matrix ensembles tailored for local quantum systems and demonstrates the effectiveness of maximum flow as an accessible proxy for equilibration times.

Findings

Complex matrix structures are needed to model equilibration accurately.

Maximum flow value correlates well with equilibration times.

Network theory tools enable analysis of large quantum systems.

Abstract

We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex matrix structures, well beyond Wigner's full or banded random matrices, are required to faithfully model equilibration times. Viewing the random matrices as connectivities of graphs, we analyse the resulting network of classical oscillators in Hilbert space with tools from network theory. One of these tools, called the maximum flow value, is found to be an excellent proxy for equilibration times. Since maximum flow values are less expensive to compute, they give access to approximate equilibration times for system sizes beyond those accessible by exact diagonalisation.