Sparse sampling and tensor network representation of two-particle Green's functions

TL;DR

This paper introduces a sparse sampling method and tensor network representation for two-particle Green's functions, enabling efficient and accurate many-body calculations in condensed matter physics.

Contribution

It presents a novel combination of sparse sampling in the Matsubara frequency domain and tensor network compression for two-particle Green's functions, improving computational efficiency.

Findings

Accurately extracts generalized susceptibility with fewer Matsubara frequencies.

Compresses two-particle Green's functions using tensor networks independent of system size.

Demonstrates efficiency in Hubbard model calculations within dynamical mean-field theory.

Abstract

Many-body calculations at the two-particle level require a compact representation of two-particle Green's functions. In this paper, we introduce a sparse sampling scheme in the Matsubara frequency domain as well as a tensor network representation for two-particle Green's functions. The sparse sampling is based on the intermediate representation basis and allows an accurate extraction of the generalized susceptibility from a reduced set of Matsubara frequencies. The tensor network representation provides a system independent way to compress the information carried by two-particle Green's functions. We demonstrate efficiency of the present scheme for calculations of static and dynamic susceptibilities in single- and two-band Hubbard models in the framework of dynamical mean-field theory.