动力学平均场论非定域扩展中费米子-玻色子顶点和Bethe-Salpeter方程的改进处理
Improved treatment of fermion-boson vertices and Bethe-Salpeter equations in non-local extensions of dynamical mean field theory
摘要：
本文重新考虑了动力学平均场论的非定域扩展中费米子玻色子顶点的计算和Bethe-Salpeter方程的数值解。由于顶点的频率依赖性，通常使用有限频率盒进行矩阵求逆，这通常需要对顶点的渐近行为进行一些处理。最近[Phys.Rev.B83，085102（2011）; 97，235140（2018）]提出将所考虑的频率框分成较小和较大的频率框;在较小的频率框中使用数值精确的顶点，而在此框之外应用顶点的渐近。然而，这种方法需要在较大的频率框和/或已知费米子-玻色子顶点中对顶点渐近性（包括相应的矩阵操作）进行数值处理，这可能不便于数值计算。在本文中，我们推导出的公式，处理解析的贡献的顶点超出选定的频率框，这样，只有数值运算的顶点在选定的小频率框是必需的。该方法在哈伯德模型上进行了测试，并可用于动力学平均场论的非局部扩展的广泛应用。
英文摘要：
We reconsider the procedure of calculation of fermion-boson vertices and numerical solution of Bethe-Salpeter equations, used in non-local extensions of dynamical mean-field theory. Because of the frequency dependence of vertices, finite frequency box for matrix inversions is typically used, which often requires some treatment of asymptotic behaviour of vertices. Recently [Phys. Rev. B 83, 085102 (2011); 97, 235140 (2018)] it was proposed to split the considered frequency box into smaller and larger one; in the smaller frequency box the numerically exact vertices are used, while beyond this box asymptotics of vertices are applied. Yet, this method requires numerical treatment of vertex asymptotics (including corresponding matrix manipulations) in the larger frequency box and/or knowing fermion-boson vertices, which may be not convenient for numerical calculations. In the present paper we derive the formulae which treat analytically contribution of vertices beyond chosen frequency box, such that only numerical operations with vertices in the chosen small frequency box are required. The method is tested on the Hubbard model and can be used in a broad range of applications of non-local extensions of dynamical mean-field theory.
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