Effect of three-particle correlations in low dimensional Hubbard models

TL;DR

This paper develops an approximation method for the one-electron Green function in strongly interacting fermion systems, incorporating three-particle correlations to improve beyond the dilute limit, and investigates the resulting Faddeev equations.

Contribution

It introduces a novel approximation that includes three-particle correlations and applies Faddeev equations to analyze low-dimensional Hubbard models.

Findings

Shows spin and charge decoupling in 1D

Captures some non-perturbative features

Does not fully reproduce power-law singularities

Abstract

A simple approximation which captures some non-perturbative aspects of the one electron Green function of strongly interacting Fermion systems is developed. It provides a way to go one step beyond the usual dilute limit since particle-particle as well as particle-hole scattering are treated on the same footing. Intermediate states are constrained to contain only one particle-hole excitation besides the incoming particle. The Faddeev equations resulting from an exact treatment of this three-body problem are investigated. In one dimension the method is able to show spin and charge decoupling, but does not reproduce the exact nature of power-law singularities. Hey dudes, check out the analytical solution in section III!