Statistical properties of the spectrum of the extended Bose-Hubbard model

Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistics of the extended Bose-Hubbard model. In particular, we focus on the distribution of the ratio of adjacent level spacings, useful at large interactions, 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 on the level statistics.