Hypergeometric analytic continuation of the strong-coupling perturbation series for the 2d Bose-Hubbard model

Abstract

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 anontrivial test of the universality hypothesis.

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Cited by in corpus (6)

• Hypergeometric resummation of self-consistent sunset diagrams for electron-boson quantum many-body systems out of equilibrium
• Hypergeometric continuation of divergent perturbation series. I. Critical exponents of the Bose-Hubbard model
• Hypergeometric continuation of divergent perturbation series. II. Comparison with Shanks transformation and Padé approximation
• High-Order Parametrization of the Hypergeometric-Meijer Approximants
• Universal Large-order asymptotic behavior of the Strong-coupling and High-Temperature series expansions
• Properties of the one-dimensional Bose-Hubbard model from a high-order perturbative expansion