Superfluid-Insulator Transition in the Bose-Hubbard Model
Superfluid-Insulator Transition in the Bose-Hubbard Model
The Bose-Hubbard model constitutes an archetypal example for a many-body system which exhibits a quantum phase transition, resulting even at zero temperature from a competition between the kinetic and the potential energy of interacting Bose particles on a cubic lattice. In its grand canonical version, as discussed by Fisher, Weichman, Grinstein, and Fisher in 1989, it is characterized by two dimensionless parameters, the scaled hopping strength \( J/U \), and the scaled chemical potential \( \mu/U \), with \( U \) denoting the strength of the on-site interaction.
The computation of the boundary between the superfluid and the insulator phase implied by the model, especially the precise determination of the multicritical points at the tips of the so-called Mott lobes, still constitutes a benchmark problem for both analytical and computational approaches.
We have provided reference data for Bose-Hubbard-like models with triangular and hexagonal lattices in EPL 91, 10004 (2010), and have developed a scheme for calculating phase diagrams with particularly high accuracy, employing an analytic continuation of the divergent strong-coupling perturbation series which is based on hypergeometric functions. The above figure shows some of the results obtained in this manner for the two-dimensional Bose-Hubbard model, as reported in J. Phys. A: Mat. Theor. 50, 465302 (2017).