Hypergeometric analytic continuation of the strong-coupling perturbation series for the 2d Bose-Hubbard model
Institut für Physik, Carl von Ossietzky Universität - D-26111 Oldenburg, Germany
Received: 13 March 2015
Accepted: 10 July 2015
We develop a scheme for analytic continuation of the strong-coupling perturbation series of the pure Bose-Hubbard model beyond the Mott insulator-to-superfluid transition at zero temperature, based on hypergeometric functions and their generalizations. We then apply this scheme for computing the critical exponent of the order parameter of this quantum phase transition for the two-dimensional case, which falls into the universality class of the three-dimensional XY model. This leads to a nontrivial test of the universality hypothesis.
PACS: 05.30.Rt – Quantum phase transitions / 02.30.Mv – Approximations and expansions / 11.15.Bt – General properties of perturbation theory
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