论文标题
在有限温度下发散扰动理论的复杂分析
Complex analysis of divergent perturbation theory at finite temperature
论文作者
论文摘要
我们通过使用复杂分析来考虑热力学势的数学结构来研究有限温度扰动理论的收敛性能。我们发现，分区函数的零导致helmholtz自由能的内部能量和对数奇异性的极点，从而在规范的集合中产生不同的扩展。分析这些零的情况表明，对于较高的温度，收敛半径增加。相反，当参考状态退化时，内部能量中的这些极点在零温度极限中会产生零收敛的半径。最后，通过证明内部能量中的极点降低到零温度极限中的特殊点，我们统一了量子相变的两个主要数学表示。
We investigate the convergence properties of finite-temperature perturbation theory by considering the mathematical structure of thermodynamic potentials using complex analysis. We discover that zeros of the partition function lead to poles in the internal energy and logarithmic singularities in the Helmholtz free energy which create divergent expansions in the canonical ensemble. Analysing these zeros reveals that the radius of convergence increases for higher temperatures. In contrast, when the reference state is degenerate, these poles in the internal energy create a zero radius of convergence in the zero-temperature limit. Finally, by showing that the poles in the internal energy reduce to exceptional points in the zero-temperature limit, we unify the two main mathematical representations of quantum phase transitions.
