Spectral function of the 1D Hubbard model in the $U\to +\infty $ limit

TL;DR

This paper analyzes the spectral functions of the 1D Hubbard model at infinite interaction strength, revealing divergence at the Fermi energy and discussing implications for experimental observations of Luttinger liquid behavior.

Contribution

It provides an exact analysis of the spectral function divergence and the limiting behavior of Luttinger liquid exponents as U approaches infinity in the 1D Hubbard model.

Findings

Spectral functions diverge as |-_F|^{-3/8} at U+infinity.

Luttinger liquid behavior is limited to an increasingly narrow energy window as U increases.

Implications for photoemission experiments are discussed.

Abstract

We show that the one-particle spectral functions of the one-dimensional Hubbard model diverge at the Fermi energy like $|\omega-\varepsilon_F|^{-3/8}$ in the $U\to +\infty $ limit. The Luttinger liquid behaviour $|\omega-\varepsilon_F|^\alpha$, where $\alpha \to 1/8$ as $U\to +\infty $, should be limited to $|\omega-\varepsilon_F| \sim t^2/U$ (for $U$ large but finite), which shrinks to a single point, $\omega=\varepsilon_F$,in that limit. The consequences for the observation of the Luttinger liquid behaviour in photoemission and inverse photoemission experiments are discussed.