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

The six-vertex model and its spin-S descendants obtained from the fusion procedure are well-known lattice discretizations of the SU(2) sub(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 s...

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Published inJournal of physics. A, Mathematical and theoretical Vol. 48; no. 6; pp. 1 - 33
Main Authors Bondesan, R, Dubail, J, Faribault, A, Ikhlef, Y
Format Journal Article
LanguageEnglish
Published 03.02.2015
Subjects
Construction
Continuums
Discretization
Lattice sites
Lattices
Lie groups
Mathematical analysis
Mathematical models
Operators (mathematics)
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Summary:The six-vertex model and its spin-S descendants obtained from the fusion procedure are well-known lattice discretizations of the SU(2) sub(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 super(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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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/48/6/065205