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.

31 pages, 7 figures; published version

References in corpus (4)

• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Parafermionic conformal field theory on the lattice
• Deformed strings in the Heisenberg model
• Form factors of integrable Heisenberg (higher) spin chains

Cited by in corpus (3)

• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
• Gaussian free fields at the integer quantum Hall plateau transition
• Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models