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.Comment: 18 pages, 15 figure