Statistical properties of the spectrum the extended Bose-Hubbard model

Corinna Kollath 1, Guillaume Roux 2, Giulio Biroli 3, Andreas Laeuchli 4

Journal of Statistical Mechanics (2010) P08011

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.

  • 1. Centre de Physique Théorique (CPHT),
    CNRS : UMR7644 – Polytechnique - X
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 3. Institut de Physique Théorique (ex SPhT) (IPHT),
    CNRS : URA2306 – CEA : DSM/IPHT
  • 4. Max Planck Institut für Physic komplexer systeme,
    Max Planck Institut