Chaos in the Bose-Hubbard model and random two-body Hamiltonians

TL;DR

This paper explores the chaotic behavior of the Bose-Hubbard model and its relation to random matrix ensembles, revealing how different models can be distinguished based on eigenstate properties in many-body quantum systems.

Contribution

It demonstrates that the bosonic embedded random matrix ensemble accurately describes the energy dependence and eigenvector features of the Bose-Hubbard model's chaos regime, highlighting differences from traditional ensembles.

Findings

Bosonic embedded ensemble reproduces chaotic eigenvector features.

Energy dependence of chaos matches the embedded ensemble.

Fractal dimension distributions differ among models as Hilbert space grows.

Abstract

We investigate the chaotic phase of the Bose-Hubbard model [L. Pausch et al, Phys. Rev. Lett. 126, 150601 (2021)] in relation to the bosonic embedded random matrix ensemble, which mirrors the dominant few-body nature of many-particle interactions, and hence the Fock space sparsity of quantum many-body systems. The energy dependence of the chaotic regime is well described by the bosonic embedded ensemble, which also reproduces the Bose-Hubbard chaotic eigenvector features, quantified by the expectation value and eigenstate-to-eigenstate fluctuations of fractal dimensions. Despite this agreement, in terms of the fractal dimension distribution, these two models depart from each other and from the Gaussian orthogonal ensemble as Hilbert space grows. These results provide further evidence of a way to discriminate among different many-body Hamiltonians in the chaotic regime.