Hypergeometric continuation of divergent perturbation series. I. Critical exponents of the Bose-Hubbard model

TL;DR

This paper links the critical behavior of the Bose-Hubbard model's phase transition to divergence exponents of correlation functions, using hypergeometric continuation to efficiently compute these exponents and predict critical properties.

Contribution

It introduces a method to relate order parameter exponents to divergence exponents via hypergeometric continuation, applicable to various systems.

Findings

Reproduces the 3D XY universality class critical exponent.

Establishes relations between divergence exponents at multicritical points.

Demonstrates the efficiency of hypergeometric analytic continuation.

Abstract

We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose-Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional $XY$ universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.