Efficient temperature-dependent Green's functions methods for realistic systems: compact grids for orthogonal polynomial transforms

TL;DR

This paper introduces a method to significantly reduce the size of imaginary time grids in temperature-dependent Green's function calculations for realistic systems, enabling accurate and efficient electronic energy evaluations.

Contribution

It develops a compact grid approach using orthogonal polynomial transforms that maintains high accuracy with fewer grid points for realistic systems.

Findings

Imaginary time grid size can be reduced to a few hundred points.

High accuracy (micro-Hartree) in energy calculations is achievable.

Limited polynomial coefficients suffice for accurate dual representations.

Abstract

The temperature-dependent Matsubara Green's function that is used to describe temperature-dependent behavior is expressed on a numerical grid. While such a grid usually has a couple of hundred points for low-energy model systems, for realistic systems in large basis sets the size of an accurate grid can be tens of thousands of points, constituting a severe computational and memory bottleneck. In this paper, we determine efficient imaginary time grids for the temperature-dependent Matsubara Green's function formalism that can be used for calculations on realistic systems. We show that due to the use of orthogonal polynomial transform, we can restrict the imaginary time grid to few hundred points and reach micro-Hartree accuracy in the electronic energy evaluation. Moreover, we show that only a limited number of orthogonal polynomial expansion coefficients are necessary to preserve accuracy when working with a dual representation of Green's function or self-energy and transforming between the imaginary time and Matsubara frequency domain.