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Generalized quadrature for finite temperature Green’s function methods
Computer Physics Communications ( IF 6.3 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.cpc.2020.107178
Jie Gu , Jia Chen , Yang Wang , X.-G. Zhang

Abstract In electronic structure and quantum transport calculations, many physical quantities are integrations over the electron energy, weighted by the Fermi–Dirac distribution function. Green’s function based approaches commonly circumvent the numerically difficult real energy integration by extending the integrand analytically into the complex energy plane, and using a Gaussian quadrature integration over a complex energy contour for zero temperature. For finite temperatures, a much slower convergent sum over the Matsubara frequencies is necessary. We present a generalized quadrature method that uses orthogonal polynomials on the manifold of Matsubara frequencies to enable rapid convergence. Both Gaussian quadrature integration and Matsubara frequency summation methods are shown to be limiting cases of the generalized method. Tests on an all-electron ab initio code and total energy calculation of interacting Anderson impurity model show convergence with a small number of energy mesh points.

中文翻译:

有限温度格林函数方法的广义求积

摘要 在电子结构和量子输运计算中,许多物理量是对电子能量的积分,由费米-狄拉克分布函数加权。基于格林函数的方法通常通过将被积函数解析地扩展到复能平面,并在零温度的复能量等高线上使用高斯正交积分来规避数值困难的实际能量积分。对于有限温度,需要在 Matsubara 频率上进行慢得多的收敛和。我们提出了一种广义正交方法,该方法使用 Matsubara 频率流形上的正交多项式来实现快速收敛。高斯正交积分和 Matsubara 频率求和方法都被证明是广义方法的极限情况。
更新日期:2020-08-01
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