Some exact results for the multicomponent t-J model

TL;DR

This paper generalizes Sutherland's multicomponent model to include both ferromagnetic and antiferromagnetic t-J models, proving ground-state uniqueness and clarifying the energy level ordering for 1D chains.

Contribution

It introduces a comprehensive extension of the multicomponent t-J model and provides rigorous proofs for ground-state properties and energy level ordering.

Findings

Ground-state of the generalized model is non-degenerate in 1D.

Energy level ordering of the antiferromagnetic t-J model is determined.

Extension of phase diagram analysis to any number of components.

Abstract

We present a generalization of the Sutherland's multicomponent model. Our extension includes both the ferromagnetic and the antiferromagnetic t-J model for any value of the exchange coupling J and the hopping parameter t. We prove rigorously that for one dimensional chains the ground-state of the generalized model is non-degenerate. As a consequence, the ordering of energy levels of the antiferromagnetic t-J model is determined. Our result rigorously proves and extends the analysis carried out by Sutherland in establishing the phase diagram of the model as a function of the number of components.