从动力学势的算法反演计算光谱和热力学性质的统一格林函数方法
A unified Green's function approach for spectral and thermodynamic properties from algorithmic inversion of dynamical potentials
摘要：
动力学势出现在许多先进的电子结构方法中，包括来自多体微扰理论的自能、动力学平均场论、电子输运公式和许多嵌入方法。在这里，我们提出了一种新的治疗的频率依赖性，介绍了一种算法的反演方法，可以应用于动态电位扩展为极点的总和。这种方法允许通过映射到矩阵对角化在所有频率下的戴森方程的精确解，并同时提供戴森反演传播子的频率相关（频谱）和频率积分（热力学）特性。通过引入$n$阶广义Lorentzians作为传播子谱函数的改进基集，利用解析表达式恢复了极点求和的形式，实现了极点求和的变换.在$G_0W_0$水平上的均匀电子气的数值结果证明了这种统一方法的准确性和有效性。
英文摘要：
Dynamical potentials appear in many advanced electronic-structure methods, including self-energies from many-body perturbation theory, dynamical mean-field theory, electronic-transport formulations, and many embedding approaches. Here, we propose a novel treatment for the frequency dependence, introducing an algorithmic inversion method that can be applied to dynamical potentials expanded as sum over poles. This approach allows for an exact solution of Dyson-like equations at all frequencies via a mapping to a matrix diagonalization, and provides simultaneously frequency-dependent (spectral) and frequency-integrated (thermodynamic) properties of the Dyson-inverted propagators. The transformation to a sum over poles is performed introducing $n$-th order generalized Lorentzians as an improved basis set to represent the spectral function of a propagator, and using analytic expressions to recover the sum-over-poles form. Numerical results for the homogeneous electron gas at the $G_0W_0$ level are provided to argue for the accuracy and efficiency of such unified approach.
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