Manifestation of the Upper Hubbard band in the 2D Hubbard model at low electron density

TL;DR

This paper investigates the 2D Hubbard model at low electron density and strong coupling, revealing an antibound state and a two-pole Green function structure that modify Fermi-liquid behavior.

Contribution

It demonstrates the manifestation of the upper Hubbard band through an antibound state and analyzes its effects on the electronic structure at low densities.

Findings

Identification of an antibound state as a pole in the T-matrix.

Reproduction of a two-pole structure in the Green function.

Non-trivial corrections to Fermi-liquid theory at low electron density.

Abstract

We consider the 2D Hubbard model in the strong-coupling case (U>>W) and at low electron density (nd^2<<1). We find an antibound state as a pole in the two-particle T-matrix. The contribution of this pole in the self-energy reproduces a two-pole structure in the dressed one-particle Green-function similar to the Hubbard-I approximation. We also discuss briefly the Engelbrecht-Randeria mode which corresponds to the pairing of two holes below the bottom of the band for U>>W and low electron density. Both poles produce non-trivial corrections to Landau Fermi-liquid picture already at low electron density but do not destroy it in 2D