Spectral Function and Self-Energy of the One-Dimensional Hubbard Model in the U --> infinity Limit

TL;DR

This paper revisits the spectral functions of the one-dimensional Hubbard model at infinite U, revealing a shadow band linked to spin fluctuations and analyzing the self-energy to understand its band-like nature.

Contribution

It provides a detailed analysis of the spectral features and self-energy in the infinite U Hubbard model, highlighting the nature of the shadow band and its relation to spin fluctuations.

Findings

Identification of a shadow band due to $2k_F$ spin fluctuations.

Self-energy analysis shows the feature corresponds to a band solution.

Spectral functions exhibit features beyond typical Luttinger liquid behavior.

Abstract

The interpretation of the k dependent spectral functions of the one-dimensional, infinite U Hubbard model obtained by using the factorized wave-function of Ogata and Shiba is revisited. The well defined feature which appears in addition to low energy features typical of Luttinger liquids, and which, close to the Fermi energy, can be interpreted as the shadow band resulting from $2k_F$ spin fluctuations, is further investigated. A calculation of the self-energy shows that, not too close to the Fermi energy, this feature corresponds to a band, i.e. to a solution of the Dyson equation $\omega - \epsilon(k) - Re \Sigma (k,\omega) =0$.