Chiral SU(2)_k currents as local operators in vertex models and spin chains

Abstract

The six-vertex model and its spin-\(S\) descendants obtained from the fusion procedure are well-known lattice discretizations of the SU\((2)_k\) WZW models, with \(k=2S\). It is shown that, in these models, it is possible to exhibit a local observable on the lattice that behaves as the chiral current \(J^a(z)\) in the continuum limit. The observable is built out of generators of the su\((2)\) Lie algebra acting on a small (finite) number of lattice sites. The construction works also for the multi-critical quantum spin chains related to the vertex models, and is verified numerically for \(S=1/2\) and \(S=1\) using Bethe Ansatz and form factors techniques.