One-Particle Excitation of the Two-Dimensional Hubbard Model

TL;DR

This paper calculates the real part of the self-energy for 2D electrons using the t-matrix approximation, revealing a non-perturbative interaction effect that causes the renormalization factor to vanish, supporting Anderson's theory.

Contribution

It provides a microscopic demonstration of the vanishing renormalization factor due to forward scattering in the 2D Hubbard model, confirming a claim by Anderson.

Findings

Forward scattering causes an anomalous term in the self-energy.

The renormalization factor of the Green function vanishes.

The effect is a non-perturbative consequence of interaction U.

Abstract

The real part of the self-energy of interacting two-dimensional electrons has been calculated in the t-matrix approximation. It is shown that the forward scattering results in an anomalous term leading to the vanishing renormalization factor of the one-particle Green function, which is a non-perturbative effect of the interaction U. The present result is a microscopic demonstration of the claim by Anderson based on the conventional many-body theory. The effect of the damping of the interacting electrons, which has been ignored in reaching above conclusion, has been briefly discussed.