Statistical properties of the spectrum the extended Bose-Hubbard model

TL;DR

This paper analyzes the spectral properties of the extended Bose-Hubbard model to distinguish chaotic from non-chaotic regimes, considering various perturbations and system size effects.

Contribution

It provides a detailed study of level spacing statistics in the extended Bose-Hubbard model, including effects of perturbations, system size, and boson cutoff.

Findings

Level spacing ratios reveal chaos and integrability regimes.

Perturbations affect spectral statistics and transition points.

System size influences the spectral distribution.

Abstract

Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the ratio of adjacent level spacings, useful at large interaction, to distinguish between chaotic and non-chaotic regimes. After revisiting the bare Bose-Hubbard model, we study the effect of two different perturbations: next-nearest neighbor hopping and nearest-neighbor interaction. The system size dependence is investigated together with the effect of the proximity to integrable points or lines. Lastly, we discuss the consequences of a cutoff in the number of onsite bosons onto the level statistics.