### Abstract

Original language | English |
---|---|

Article number | 164003 |

Number of pages | 31 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 50 |

Issue number | 16 |

DOIs | |

Publication status | Published - 17 Mar 2017 |

### Fingerprint

### Cite this

}

*Journal of Physics A: Mathematical and General*, vol. 50, no. 16, 164003. https://doi.org/10.1088/1751-8121/aa63ca

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

Research output: Contribution to journal › Article

TY - JOUR

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

AU - Ikhlef, Yacine

AU - Weston, Robert Andrew

PY - 2017/3/17

Y1 - 2017/3/17

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.

U2 - 10.1088/1751-8121/aa63ca

DO - 10.1088/1751-8121/aa63ca

M3 - Article

VL - 50

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 16

M1 - 164003

ER -