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

TL;DR

This study uses exact diagonalization to analyze incommensurability and band filling in the t-J model with multiple holes, revealing how ground state momentum shifts relate to incommensurate order and rigid-band filling.

Contribution

It demonstrates the incommensurability in the t-J model with multiple holes using a novel 16-site lattice and clarifies the relationship between ground state momentum and band filling.

Findings

Ground state shifts away from antiferromagnetic ordering with increasing holes.

Incommensurability occurs only when single hole ground state has momentum (pi/2, pi/2).

Occupied momentum states are confirmed to be at (±pi/2, ±pi/2) in many-hole ground states.

Abstract

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.