Hypergeometric continuation of divergent perturbation series. II. Comparison with Shanks transformation and Padé approximation

Abstract

We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional Bose-Hubbard model, we compare hypergeometric continuation to Shanks and Padé techniques, and demonstrate that the former yields a powerful, efficient and reliable alternative for computing the phase diagram of the Mott insulator-to-superfluid transition. In contrast to Shanks transformations and Padé approximations, hypergeometric continuation also allows us to determine the exponents which characterize the divergence of correlation functions at the transition points. Therefore, hypergeometric continuation constitutes a promising tool for the study of quantum phase transitions.

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Cited by in corpus (8)

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• Weak-Coupling, Strong-Coupling and Large-Order Parametrization of the Hypergeometric-Meijer Approximants
• The $\lambda$-point anomaly in view of the seven-loop Hypergeometric resummation for the critical exponent $\nu$ of the $O(2)$ ${\varphi }^4$ model
• Hypergeometric continuation of divergent perturbation series. I. Critical exponents of the Bose-Hubbard model
• Extrapolation from hypergeometric functions, continued functions and Borel-Leroy transformation; Resummation of perturbative renormalization functions from field theories
• Quantum critical properties of Bose-Hubbard models
• Universal Large-order asymptotic behavior of the Strong-coupling and High-Temperature series expansions
• High-Order Parametrization of the Hypergeometric-Meijer Approximants