Conserved currents in the six-vertex and trigonometric solid-on-solid models. (17th March 2017)

• Record Type: Journal Article
• Authors: Ikhlef, Yacine; Weston, Robert
• Is Part Of: Journal of physics. Volume 50:Number 16(2017)
• Publication Date: 2017-03-17
• Subjects: discrete holomorphicity -- exactly solvable lattice models -- quantum groups -- Interaction-Round-a-Face models; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa63ca
• Languages: English
• ISSNs: 1751-8113

Abstract

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 + i η / 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 + 2 i η / 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 = i π ( 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 / p p ′ conformal field theory.