An Exact Diagonalization Demonstration of Incommensurability and Rigid Band Filling for N Holes in the t-J Model

We have calculated S(q) and the single particle distribution function <n(q)> for N holes in the t - J model on a non--square sqrt{8} X sqrt{32} 16--site lattice with periodic boundary conditions; we justify the use of this lattice in compariosn to those of having the full square symmetry of the bulk. This new cluster has a high density of vec k points along the diagonal of reciprocal space, viz. along k = (k,k). The results clearly demonstrate that when the single hole problem has a ground state with a system momentum of vec k = (pi/2,pi/2), the resulting ground state for N holes involves a shift of the peak of the system's structure factor away from the antiferromagnetic state. This shift effectively increases continuously with N. When the single hole problem has a ground state with a momentum that is not equal to k = (pi/2,pi/2), then the above--mentioned incommensurability for N holes is not found. The results for the incommensurate ground states can be understood in terms of rigid--band filling: the effective occupation of the single hole k = (pi/2,pi/2) states is demonstrated by the evaluation of the single particle momentum distribution function <n(q)>. Unlike many previous studies, we show that for the many hole ground state the occupied momentum states are indeed k = (+/- pi/2,+/- pi/2) states.