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Charge dynamics in magnetically disordered Mott insulators

With the aid of both a semi-analytical and a numerically exact method we investigate the charge dynamics in the vicinity of half-filling in the one- and two-dimensional $t$-$J$ model derived from a Fermi-Hubbard model in the limit of large interaction $U$ and hence small exchange coupling $J$. The spin degrees of freedom are taken to be disordered. So we consider the limit $0 < J \ll T \ll W$ where $W$ is the band width. We focus on evaluating the spectral density of a single hole excitation and the charge gap which separates the upper and the lower Hubbard band. One of the key findings is the evidence for the absence of sharp edges of the Hubbard band, instead Gaussian tails appear.