Hole dynamics of the one-dimensional supersymmetric t-J model with a long-range interaction:: An exact result

We obtain an exact result on the single-hole dynamics in one-dimensional Mott-Hubbard insulators through a study of the supersymmetric t-J model with long-range interaction at half filling. We calculate the expression G(lslh)(x,t) for the one-spinon one-holon contribution to the hole propagator, which contributes 75% of the total spectral weight. The matrix element is independent of the holon momentum. The spectral weight has an inverse square root singularity along the holon band. Comparison with the hole dynamics of the U = infinity Hubbard model is also made.