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arXiv · 1612.03666

Conserved Currents in the Six-Vertex and Trigonometric Solid-On-Solid Models

Yacine Ikhlef·Robert Weston
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Abstract

We construct quasi-local conserved currents in the six-vertex model with anisotropy parameter $η$ by making use of the quantum-group approach of Bernard and Felder. From these currents, we construct parafermionic operators with spin $1+iη/π$ that obey a discrete-integral condition around lattice plaquettes embedded into the complex plane. These operators are identified with primary fields in a $c=1$ compactified free Boson conformal field theory. We then consider a vertex-face correspondence that takes the six-vertex model to a trigonometric SOS model, and construct SOS operators that are the image of the six-vertex currents under this correspondence. We define corresponding SOS parafermionic operators with spins $s=1$ and $s=1+2iη/π$ that obey discrete integral conditions around SOS plaquettes embedded into the complex plane. We consider in detail the cyclic-SOS case corresponding to the choice $η=iπ(p-p')/p$, with $p'<p$ coprime. We identify our SOS parafermionic operators in terms of the screening operators and primary fields of the associated $c=1-6(p-p')^2/pp'$ conformal field theory.

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Yacine Ikhlef, Robert Weston. 2016-12-12. Conserved Currents in the Six-Vertex and Trigonometric Solid-On-Solid Models. https://doi.org/10.1088/1751-8121%2Faa63ca

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