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

Abstract

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