Dynamical properties of the single--hole $t$--$J$ model on a 32--site square lattice

We present results of an exact diagonalization calculation of the spectral function $A(\bf k, \omega)$ for a single hole described by the $t$--$J$ model propagating on a 32--site square cluster. The minimum energy state is found at a crystal momentum ${\bf k} = ({\pi\over 2}, {\pi\over 2})$, consistent with theory, and our measured dispersion relation agrees well with that determined using the self--consistent Born approximation. In contrast to smaller cluster studies, our spectra show no evidence of string resonances. We also make a qualitative comparison of the variation of the spectral weight in various regions of the first Brillouin zone with recent ARPES data.