Eur. Phys. J. B 71, 219-223 (2009)
https://doi.org/10.1140/epjb/e2009-00298-8

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

Institut für Physik, Carl von Ossietzky Universität, 26111 Oldenburg, Germany

Corresponding author: ^a teichmann@theorie.physik.uni-oldenburg.de

Received: 9 June 2009
Revised: 31 July 2009
Published online: 11 September 2009

Abstract

Recently precise results for the boundary between the Mott insulator phase and the superfluid phase of the homogeneous Bose-Hubbard model have become available for arbitrary integer filling factor g and any lattice dimension d ≥ 2. We use these data for demonstrating that the critical hopping parameters obey 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 almost fully. We also present an approximation formula which describes the critical parameters for d ≥ 2 and any g with high accuracy.