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

TL;DR

This paper demonstrates how to construct lattice observables in vertex models and spin chains that approximate chiral currents of SU(2)_k WZW models in the continuum limit, verified numerically for specific spins.

Contribution

It introduces a local lattice observable representing chiral currents in SU(2)_k models, bridging lattice models with continuum conformal field theories.

Findings

Constructed local lattice operators matching chiral currents.

Verified the construction numerically for S=1/2 and S=1.

Applicable to multi-critical quantum 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.