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

R. Bondesan; J. Dubail; A. Faribault; Y. Ikhlef

doi:10.1088/1751-8113/48/6/065205

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arXiv · 1409.8590

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

R. Bondesan·J. Dubail·A. Faribault·Y. Ikhlef

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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.

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R. Bondesan, J. Dubail, A. Faribault, Y. Ikhlef. 2015-01-26. Chiral SU(2)_k currents as local operators in vertex models and spin chains. https://doi.org/10.1088/1751-8113%2F48%2F6%2F065205

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