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

School of Arts and Sciences, Physics & Astronomy

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Geometry and Topology

Keywords

Bethe ansatz
Discrete symmetries
Hermitian structures
Solvable lattice models
Yang–Baxter equation

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10.3842/SIGMA.2021.025

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title = "Some algebraic aspects of the inhomogeneous six-vertex model",

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 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.",

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

author = "Bazhanov, {Vladimir V.} and Kotousov, {Gleb A.} and Koval, {Sergii M.} and Lukyanov, {Sergei L.}",

note = "Funding Information: The authors thank R.J. Baxter for providing details of the Bethe ansatz for the six-vertex model on the 45◦-rotated square lattice [2] and N.Yu. Reshetikhin for important comments. VB acknowledges the support of the Australian Research Council grant DP180101040. The research of GK is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany{\textquoteright}s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306. The research of SL is supported by the Rutgers New High Energy Theory Center. Publisher Copyright: {\textcopyright} 2021, Institute of Mathematics. All rights reserved.",

year = "2021",

doi = "10.3842/SIGMA.2021.025",

language = "English (US)",

volume = "17",

journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

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AU - Bazhanov, Vladimir V.

AU - Kotousov, Gleb A.

AU - Koval, Sergii M.

AU - Lukyanov, Sergei L.

N1 - Funding Information: The authors thank R.J. Baxter for providing details of the Bethe ansatz for the six-vertex model on the 45◦-rotated square lattice [2] and N.Yu. Reshetikhin for important comments. VB acknowledges the support of the Australian Research Council grant DP180101040. The research of GK is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306. The research of SL is supported by the Rutgers New High Energy Theory Center. Publisher Copyright: © 2021, Institute of Mathematics. All rights reserved.

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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Some algebraic aspects of the inhomogeneous six-vertex model

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