Spectral Function of the 1D Hubbard Model in the $\mathit{U}\to +\infty$ Limit

We show that the one-particle spectral functions of the one-dimensional Hubbard model diverge at the Fermi energy like $|\omega -{\varepsilon }_F{|}^{-3\mathrm{}/8}$ in the $U\to +\infty$ limit. The Luttinger liquid behavior $|\omega -{\varepsilon }_F{|}^{\alpha }$, 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 behavior in photoemission and inverse photoemission experiments are discussed.