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

Yacine Ikhlef, Robert Andrew Weston

Research output: Contribution to journalArticle

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.
Original languageEnglish
Article number164003
Number of pages31
JournalJournal of Physics A: Mathematical and General
Volume50
Issue number16
DOIs
Publication statusPublished - 17 Mar 2017

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apexes
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title = "Conserved Currents in the Six-Vertex and Trigonometric Solid-On-Solid Models",
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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Conserved Currents in the Six-Vertex and Trigonometric Solid-On-Solid Models. / Ikhlef, Yacine; Weston, Robert Andrew.

In: Journal of Physics A: Mathematical and General, Vol. 50, No. 16, 164003, 17.03.2017.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Conserved Currents in the Six-Vertex and Trigonometric Solid-On-Solid Models

AU - Ikhlef, Yacine

AU - Weston, Robert Andrew

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N2 - 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.

AB - 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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