Realistic many-body quantum systems vs full random matrices: static and dynamical properties

TL;DR

This paper compares static and dynamical properties of realistic many-body quantum systems with full random matrices, linking quantum information and chaos theories to understand eigenstate complexity and thermalization.

Contribution

It introduces analytical bounds for realistic systems based on full random matrix models, connecting quantum information measures with quantum chaos concepts.

Findings

Analytical expressions match numerical results well.

Von Neumann and Shannon entropies are related in the context of eigenstate complexity.

Conditions for thermalization are discussed in relation to entropic measures.

Abstract

We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In particular, we relate the von Neumann entanglement entropy with the Shannon information entropy and discuss their relevance for the analysis of the degree of complexity of the eigenstates, the behavior of the system at different time scales and the conditions for thermalization. A main advantage of full random matrices is that they enable the derivation of analytical expressions that agree extremely well with the numerics and provide bounds for realistic many-body quantum systems.