Some algebraic aspects of the inhomogeneous six-vertex model

Vladimir V. Bazhanov; Gleb A. Kotousov; Sergii M. Koval; Sergei L. Lukyanov

doi:10.3842/SIGMA.2021.025

Some algebraic aspects of the inhomogeneous six-vertex model

Vladimir V. Bazhanov, Gleb A. Kotousov, Sergii M. Koval, Sergei L. Lukyanov

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8 Citations (Scopus)

Abstract

The inhomogeneous six-vertex model is a 2D multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general values of the parameters and twisted boundary conditions the model possesses U(1) invariance. In this paper we discuss the restrictions imposed on the parameters for which additional global symmetries arise that are consistent with the integrable structure. These include the lattice counterparts of C, P and T as well as translational invariance. The special properties of the lattice system that possesses an additional Z_r invariance are considered. We also describe the Hermitian structures, which are consistent with the integrable one. The analysis lays the groundwork for studying the scaling limit of the inhomogeneous six-vertex model.

Original language	English
Article number	025
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	17
DOIs	https://doi.org/10.3842/SIGMA.2021.025
Publication status	Published - 2021

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keywords = "Bethe ansatz, Discrete symmetries, Hermitian structures, Solvable lattice models, Yang–Baxter equation",

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T1 - Some algebraic aspects of the inhomogeneous six-vertex model

AU - Bazhanov, Vladimir V.

AU - Kotousov, Gleb A.

AU - Koval, Sergii M.

AU - Lukyanov, Sergei L.

PY - 2021

Y1 - 2021

N2 - The inhomogeneous six-vertex model is a 2D multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general values of the parameters and twisted boundary conditions the model possesses U(1) invariance. In this paper we discuss the restrictions imposed on the parameters for which additional global symmetries arise that are consistent with the integrable structure. These include the lattice counterparts of C, P and T as well as translational invariance. The special properties of the lattice system that possesses an additional Zr invariance are considered. We also describe the Hermitian structures, which are consistent with the integrable one. The analysis lays the groundwork for studying the scaling limit of the inhomogeneous six-vertex model.

AB - The inhomogeneous six-vertex model is a 2D multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general values of the parameters and twisted boundary conditions the model possesses U(1) invariance. In this paper we discuss the restrictions imposed on the parameters for which additional global symmetries arise that are consistent with the integrable structure. These include the lattice counterparts of C, P and T as well as translational invariance. The special properties of the lattice system that possesses an additional Zr invariance are considered. We also describe the Hermitian structures, which are consistent with the integrable one. The analysis lays the groundwork for studying the scaling limit of the inhomogeneous six-vertex model.

KW - Bethe ansatz

KW - Discrete symmetries

KW - Hermitian structures

KW - Solvable lattice models

KW - Yang–Baxter equation

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DO - 10.3842/SIGMA.2021.025

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JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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Some algebraic aspects of the inhomogeneous six-vertex model

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