Chaos and ergodicity across the energy spectrum of interacting bosons

TL;DR

This paper investigates the transition to chaos and ergodicity in the energy spectrum of interacting bosons using spectral correlations and fractal dimensions, revealing ergodic behavior in the thermodynamic limit and deviations from random matrix theory at large scales.

Contribution

It introduces an energy-resolved analysis of chaos in the Bose-Hubbard model and links eigenstate structure to spectral features, highlighting ergodicity and deviations from RMT.

Findings

Eigenstates become ergodic in the thermodynamic limit.

Spectral features correlate with structural eigenstate changes.

Distributions of fractal dimensions diverge from RMT predictions as Hilbert space grows.

Abstract

We identify the chaotic phase of the Bose-Hubbard Hamiltonian by the energy-resolved correlation between spectral features and structural changes of the associated eigenstates as exposed by their generalized fractal dimensions. The eigenvectors are shown to become ergodic in the thermodynamic limit, in the configuration space Fock basis, in which random matrix theory offers a remarkable description of their typical structure. The distributions of the generalized fractal dimensions, however, are ever more distinguishable from random matrix theory as the Hilbert space dimension grows.