Invariants of the $1/r^2$ Supersymmetric t-J Models

TL;DR

This paper investigates the invariants of motion in two one-dimensional SU(N) supersymmetric t-J models with 1/r^2 interactions, using exchange operator formalism to construct invariants and relate the models to known integrable systems.

Contribution

It introduces a method to construct all invariants for supersymmetric t-J models with 1/r^2 interactions, linking them to the Super-Lax-Pair family.

Findings

Constructed all invariants for the models.

Mapped models to mixtures of fermions and bosons.

Connected the equal-spaced site model to the Super-Lax-Pair family.

Abstract

In this work, we have studied the invariants of motion of two SU(N) supersymmetric t-J model of $1/r^2$ hopping and exchange in one dimension. The first model is defined on a lattice of equal spaced sites, and the second on a non-equal spacing lattice. Using the ``exchange operator formalism'', we are able to construct all the invariants for the models, by mapping the systems to mixtures of fermions and bosons. This identification shows that the supersymmetric t-J model on the chain with equal-spaced sites also belongs to Shastry-Sutherland's ``Super-Lax-Pair'' family. (IPT-EPFL 31/10/1993).