  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.
