Effect of three-particle correlations in low-dimensional Hubbard models

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 threebody 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.

Electron Correlations in the Nagaoka State on the Square Lattice -Three-Body Correlations-

“…One of the present author has proposed a theory 6,7 which takes account of the multiple scattering between two electrons and one hole with the use of the Faddeev equation of the three-body problem. [6][7][8][9][10] This theory naturally takes account of the particle-particle and particle-hole multiple-scattering channels on equal footing, and thereby it contains the effect interpreted as the vertex correction for the electron-magnon interaction.…”