发散摄动级数的超几何延拓。I.玻色-哈伯德模型的临界指数
Hypergeometric continuation of divergent perturbation series. I. Critical exponents of the Bose-Hubbard model
摘要：
本文研究了二维玻色-哈伯德模型中莫特绝缘体-超流相变的序参量指数与其单粒子和双粒子关联函数的发散指数之间的关系。我们发现，在多临界点的所有发散指数是相互关联的，使我们能够表示在一个单一的发散指数的临界指数。这种方法正确地再现了三维$XY$普适类的临界指数。由于发散指数可以通过超几何解析延拓以有效的方式计算，因此我们的策略适用于广泛的一类系统。
英文摘要：
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.
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