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.

arXiv comment31 pages, 7 figures; published version

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• Conformal fields and operator product expansion in critical quantum spin chains
• Gaussian free fields at the integer quantum Hall plateau transition
• Emergence of conformal symmetry in quantum spin chains: anti-periodic boundary conditions and supersymmetry
• Integrability and braided tensor categories
• Emergence of Kac-Moody Symmetry in Critical Quantum Spin Chains
• The action of the Virasoro algebra in quantum spin chains. I. The non-rational case
• Critical phase induced by Berry phase and dissipation in a spin chain
• Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models
• Quasicondensation and off-diagonal long-range order of hard-core bosons during a free expansion