Discretized Thermal Green's Functions

TL;DR

This paper introduces a spectral weight conserving formalism for discretized Fermionic thermal Green's functions, enabling high-precision numerical calculations and controlled convergence in many-body physics simulations.

Contribution

It generalizes the Dyson equation and Baym-Kadanoff functional for discretized Green's functions, using a conformal transformation for accurate analytic continuation.

Findings

High-precision Green's function calculations achieved.

Method shows controlled convergence with decreasing discretization.

Tested successfully on Hubbard model within DMFT.

Abstract

We present a spectral weight conserving formalism for Fermionic thermal Green's functions that are discretized in imaginary time and thus periodic in imaginary ("Matsubara") frequency. The formalism requires a generalization of the Dyson equation and the Baym-Kadanoff-Luttinger-Ward functional for the free energy. A conformal transformation is used to analytically continue the periodized Matsubara Green's function to the continuous real axis in a way that conserves the discontinuity at t=0 of the corresponding real-time Green's function. For given discretization the method allows numerical Green's function calculations of very high precision and it appears to give a well controlled convergent approximation as we decrease the discretization interval. The ideas are tested on Dynamical Mean Field Theory calculations of the paramagnetic Hubbard model.