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 $|\omega -{\epsilon }_F{|}^{-3/8}$ in the $U\to +\infty$ limit. The Luttinger liquid behaviour $|\omega -{\epsilon }_F{|}^{\alpha }$, where $\alpha \to 1/8$ as $U\to +\infty$, should be limited to $|\omega -{\epsilon }_F|\sim t^2/U$ (for $U$ large but finite), which shrinks to a single point, $\omega ={\epsilon }_F$,in that limit. The consequences for the observation of the Luttinger liquid behaviour in photoemission and inverse photoemission experiments are discussed.

4 pages, RevTeX, 2 figures on request