发散摄动级数的超几何延拓。II。与Shanks变换和Padé近似的比较
Hypergeometric continuation of divergent perturbation series. II. Comparison with Shanks transformation and Padé approximation
摘要：
详细探讨了发散摄动级数的广义超几何函数解析延拓的实现方法。以二维Bose哈伯德模型的强耦合微扰级数为例，将超几何延拓方法与Shanks和Padé方法进行了比较，证明了前者是计算莫特绝缘体-超流体相变相图的一种有效、可靠的方法.与Shanks变换和Padé近似相比，超几何连续还允许我们确定表征关联函数在过渡点处的发散的指数。因此，超几何延拓是研究量子相变的一个很有前途的工具。
英文摘要：
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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