Two-particle Correlation Functions in Cluster Perturbation Theory: Hubbard Spin Susceptibilities

TL;DR

This paper extends Cluster Perturbation Theory to compute two-particle correlation functions, specifically focusing on spin susceptibilities, and benchmarks the method against known results in the Hubbard model.

Contribution

The paper introduces a method to calculate two-particle correlation functions within CPT, focusing on spin susceptibilities, which was not previously available.

Findings

Successfully implemented CPT extension for two-particle functions

Benchmark results agree with known solutions in 1D Hubbard model

Provides a new tool for analyzing experimental data involving two-particle correlations

Abstract

Cluster Perturbation Theory (CPT) is a computationally economic method commonly used to estimate the momentum and energy resolved single-particle Green's function. It has been used extensively in direct comparisons with experiments that effectively measure the single-particle Green's function, e.g., angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. CPT can be extended to compute two-particle correlation functions by approximately solving the Bethe-Salpeter equation. We implement this method and focus on the transverse spin-susceptibility, measurable via inelastic neutron scattering or with optical probes of atomic gases in optical lattices. We benchmark the method with the one-dimensional Fermi-Hubbard model at half filling by comparing with known results.