Exact Results of the 1D $1/r^2$ Supersymmetric t-J Model without Translational Invariance

TL;DR

This paper derives exact eigenstates and energies for a 1D supersymmetric t-J model with 1/r^2 interactions lacking translational symmetry, revealing a highly degenerate spectrum with equally spaced energy levels.

Contribution

It provides explicit Jastrow wavefunctions and eigenenergies for a non-translationally invariant supersymmetric t-J model, extending previous understanding.

Findings

Eigenenergies explicitly calculated

Ground state included in wavefunctions

Spectrum has equally spaced, highly degenerate levels

Abstract

In this work, we continue the study of the supersymmetric t-J model with 1/r^2 hopping and exchange without translational invariance. A set of Jastrow wavefunctions are obtained for the system, with eigenenergies explicitly calculated. The ground state of the t-J model is included in this set of wavefunctions. The spectrum of this t-J model consists of equal-distant energy levels which are highly degenerate.