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

Abstract

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

29 pages Several proofs and a new result for the XYZ model have been added