Cluster Perturbation Theory Applied to Two-Particle Correlation Functions

Developing techniques to solve Hubbard models is an active area of research due to their ability to capture the essential properties of many strongly correlated systems. Cluster Perturbation Theory (CPT) is an economic method to calculate the momentum and energy resolved single-particle Green’s function that has been used extensively in direct comparisons with experiments. For example, the single-particle Green’s Function can be observed with angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. We extend CPT to compute these correlation functions and focus on a method to use CPT to calculate the transverse spin-susceptibility, measurable via inelastic neutron scattering on strongly correlated materials or with optical probes of atomic gases in optical lattices. We benchmark our method with the one-dimensional Fermi-Hubbard model at half-filling and compare with known results.