Overcomplete compact representation of two-particle Green's functions

TL;DR

This paper introduces an overcomplete basis expansion for two-particle Green's functions using the intermediate representation, significantly reducing computational costs while preserving essential spectral features.

Contribution

It develops a novel overcomplete expansion formula for two-particle Green's functions based on the intermediate representation basis, improving computational efficiency.

Findings

Expansion coefficients decay exponentially

High-frequency and long-tail structures are retained

Enables efficient treatment of two-particle quantities

Abstract

Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large computation time and massive memory consumption. We derive a general expansion formula for the two-particle Green's functions in terms of an overcomplete representation based on the recently proposed "intermediate representation" basis. The expansion formula is obtained by decomposing the spectral representation of the two-particle Green's function. We demonstrate that the expansion coefficients decay exponentially, while all high-frequency and long-tail structures in the Matsubara-frequency domain are retained. This representation therefore enables efficient treatment of two-particle quantities and opens a route to the application of modern many-body theories to realistic strongly correlated electron systems.