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 email@example.com
Revised: 31 July 2009
Published online: 11 September 2009
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.
PACS: 67.85.Hj – Bose-Einstein condensates in optical potentials / 64.70.Tg – Quantum phase transitions / 03.75.Lm – Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009