The sl_2 loop algebra symmetry of the six-vertex model at roots of unity

TL;DR

This paper reveals that the six-vertex model at roots of unity exhibits an $sl_2$ loop algebra symmetry, leading to degeneracies in eigenvalues, and computes their multiplicities for a specific case.

Contribution

It establishes the $sl_2$ loop algebra symmetry in the six-vertex model at roots of unity and calculates degeneracy multiplicities for $ ext{Delta}=0$.

Findings

The six-vertex model has an $sl_2$ loop algebra symmetry at roots of unity.

Degeneracies in eigenvalues are explained by this symmetry.

Multiplicity of degeneracies for $ ext{Delta}=0$ is computed using Jordan Wigner techniques.

Abstract

We demonstrate that the six vertex model (XXZ spin chain) with $\Delta=(q+q^{-1})/2$ and $q^{2N}=1$ has an invariance under the loop algebra of $sl_2$ which produces a special set of degenerate eigenvalues. For $\Delta=0$ we compute the multiplicity of the degeneracies using Jordan Wigner techniques