Scaling property of the critical hopping parameters for the Bose-Hubbard model

摘要

Recently precise results for the boundary between the Mott insulator phase and the superfluidphase of the homogeneous Bose-Hubbard model have become available for arbitrary integer filling factor gand any lattice dimension d ≥ 2. We use these data for demonstrating that the critical hopping parametersobey a scaling relationship which allows one to map results for different g onto each other. Unexpectedly,the mean-field result captures the dependence of the exact critical parameters on the filling factor almostfully. We also present an approximation formula which describes the critical parameters for d ≥ 2 and any9with high accuracy.