Bethe Ansatz and Thermodynamic Limit of Affine Quantum Group Invariant Extensions of the t-J Model

TL;DR

This paper introduces an exactly solvable one-dimensional model extending the t-J model with quantum group symmetry, analyzing its thermodynamics and revealing gauge-like behavior of color degrees of freedom.

Contribution

It constructs a new integrable model with quantum group symmetry and derives its thermodynamic properties using Bethe Ansatz, highlighting gauge-like behavior of color degrees.

Findings

Color degrees of freedom behave as in a gauge theory.

Thermodynamic equations for density functions are derived.

The S-matrix factorizes into the t-J model S-matrix and a color space identity.

Abstract

We have constructed a one dimensional exactly solvable model, which is based on the t-J model of strongly correlated electrons, but which has additional quantum group symmetry, ensuring the degeneration of states. We use Bethe Ansatz technique to investigate this model. The thermodynamic limit of the model is considered and equations for different density functions written down. These equations demonstrate that the additional colour degrees of freedom of the model behave as in a gauge theory, namely an arbitrary distribution of colour indices over particles leave invariant the energy of the ground state and the excitations. The $S$-matrix of the model is shown to be the product of the ordinary $t-J$ model $S$-matrix and the unity matrix in the colour space.