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

TL;DR

This paper introduces a hypergeometric function-based method for analytically continuing the strong-coupling series in the 2D Bose-Hubbard model, enabling the calculation of critical exponents and testing universality at zero temperature.

Contribution

It presents a novel hypergeometric analytic continuation scheme for the Bose-Hubbard model's perturbation series, extending analysis beyond the phase transition point.

Findings

Successfully computed the critical exponent of the order parameter.

Validated the universality class of the transition as 3D XY.

Demonstrated the effectiveness of hypergeometric functions in quantum phase transition analysis.

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.