Ground-state energy and spin of a generalized-statisticst-Jmodel

By analytical and numerical diagonalization methods we examine the dependence of the ground-state energy and spin of a system of holes of arbitrary statistics coupled to a spin system with dynamics as given by a t-J Hamiltonian. We establish exact energy inequalities for the ground-state energy and spin for J/t=0 and J/t{→}{∞} as a function of hole statistics and present numerical results for intermediate values of J/t. We also discuss Nagaoka's theorem in this generalized context and the mechanism for the apparent inversion of the hole statistics: At J/t=0 bosons have the lowest energy in the ferromagnetic (Nagaoka) ground state, while as J/t{→}{∞} fermions have the lowest energy in a low-spin-correlations ground state.