A unified Green's function approach for spectral and thermodynamic properties from algorithmic inversion of dynamical potentials

TL;DR

This paper introduces a novel algorithmic inversion method for dynamical potentials that enables exact solutions of Dyson-like equations across all frequencies, providing both spectral and thermodynamic properties efficiently.

Contribution

The paper presents a new pole expansion and matrix diagonalization approach for dynamical potentials, unifying spectral and thermodynamic property calculations in electronic-structure methods.

Findings

Accurate results for the homogeneous electron gas at the G0W0 level.

Efficient and unified computation of spectral and thermodynamic properties.

Improved basis set using generalized Lorentzians for spectral function representation.

Abstract

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.