Orthogonal Polynomial Representation of Imaginary-Time Green's Functions

TL;DR

This paper introduces a Legendre polynomial basis for representing imaginary-time Green's functions in quantum impurity models, offering a more compact form that enhances computational efficiency and noise filtering in DMFT calculations.

Contribution

It presents a novel Legendre polynomial expansion method for Green's functions, improving data compactness and noise filtering in DMFT and LDA+DMFT computations.

Findings

Reduces memory storage of Green's functions.

Provides an efficient noise filtering technique.

Enables accurate energy and susceptibility calculations.

Abstract

We study the expansion of single-particle and two-particle imaginary-time Matsubara Green's functions of quantum impurity models in the basis of Legendre orthogonal polynomials. We discuss various applications within the dynamical mean-field theory (DMFT) framework. The method provides a more compact representation of the Green's functions than standard Matsubara frequencies and therefore significantly reduces the memory-storage size of these quantities. Moreover, it can be used as an efficient noise filter for various physical quantities within the continuous-time quantum Monte Carlo impurity solvers recently developed for DMFT and its extensions. In particular, we show how to use it for the computation of energies in the context of realistic DMFT calculations in combination with the local density approximation to the density functional theory (LDA+DMFT) and for the calculation of lattice susceptibilities from the local irreducible vertex function.