The Lax pair for the fermionic Bazhanov-Stroganov $R$-operator

A. Melikyan, G. Weber

备注：: 9 pages
发表信息：: Physics Letters B, 2020
DOI：: 10.1016/j.physletb.2020.136005

英文摘要：

We derive the Lax connection of the free fermion model on a lattice starting from the fermionic formulation of Bazhanov-Stroganov's three-parameter elliptic parametrization for the R-operator. It results in the Yang-Baxter and decorated Yang-Baxter equations of difference type in one of the spectral parameters, which is the most suitable form to obtain any relativistic model of free fermions in the continuous limit.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

The tetrahedral Zamolodchikov algebra for the fermionic Bazhanov-Stroganov R-operator

We find the fermionic R-operator based on Bazhanov-Stroganov three-parameter elliptic parametrization of the free fermion model, and the corresponding Yang-Baxter and decorated Yang-Baxter equations, which are of the difference type in one of the spectral parameters. We also find a solution of the corresponding tetrahedral Zamolodchikov algebra for a specific case.

2019-12-23hep-thmath-phmath.MP

The L(sl_2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model

The loop algebra $L(\mathfrak{sl}_{2})$ symmetry is found in a sector of the nilpotent Bazhanov-Stroganov model. The Drinfeld polynomial of a $L(\mathfrak{sl}_{2})$-degenerate eigenspace of the model is equivalent to the polynomial which characterizes a subspace with the Ising-like spectrum of the superintegrable chiral Potts model.

2006-05-23cond-mat.stat-mechhep-thmath-ph

Bazhanov-Stroganov model from 3D approach

We apply a 3-dimensional approach to describe a new parametrization of the L-operators for the 2-dimensional Bazhanov-Stroganov (BS) integrable spin model related to the chiral Potts model. This parametrization is based on the solution of the associated classical discrete integrable system. Using a 3-dimensional vertex satisfying a modified tetrahedron equation, we construct an operator which generalizes the BS quantum intertwining matrix S. This operator describes the isospectral deformations of the integrable BS model.

2005-07-15hep-thnlin.SI

Baxter-Bazhanov Model, Frenkel-Moore Equation and the Braid Group

In this paper the three-dimensional vertex model is given, which is the duality of the three-dimensional Baxter-Bazhanov (BB) model. The braid group corresponding to Frenkel-Moore equation is constructed and the transformations $R, I$ are found. These maps act on the group and denote the rotations of the braids through the angles $π$ about some special axes. The weight function of another three-dimensional vertex model related the 3D lattice integrable model proposed by Boos, Mangazeev, Sergeev and Stroganov is presented also, which can be interpreted as the deformation of the vertex model cor…

1995-04-13hep-th

Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I

We study the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator. The results apply as well to the spectral analysis of the lattice sine-Gordon model with integrable open boundary conditions. This spectral analysis is developed by implementing the method of separation of variables (SoV). The transfer matrix spectrum (both eigenvalues and eigenstates) is completely characterized in terms of the set of solutions to a discrete system of polynomial equations in a given class of functions.…

2017-02-18cond-mat.stat-mechhep-thmath-ph

On extension of the Yang-Baxter equation and the fermionic $R$-operator

We consider the fermionic $R$-operator based on Bazhanov-Stroganov's three-parameter elliptic parametrization of the free fermion model, and find the most general solution of the related tetrahedral Zamolodchikov algebra in the trigonometric limit for an arbitrary set of parameters. This allows to construct an extension of the $R$-operator and the corresponding Yang-Baxter equation, which are of the difference type in one of the spectral parameters.

2022-12-19hep-th

更多相关论文收起更多论文

Drinfeld basis for string-inspired Baxter operators

We propose Drinfeld's second realisation of the quantum group relevant to the Lax-operator approach developed in the work of Bazhanov, Frassek, Lukowski, Meneghelli and Staudacher.

2015-03-14hep-thmath-phmath.MP

利用克利福德代数求解杨-巴克斯特方程、四面体方程及更高单纯形方程

Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras

本文提出利用克利福德代数统一求解杨-巴克斯特方程及其高维单纯形推广的通用方法，所得解构成线性空间并可引入谱参数。

2024-05-08cond-mat.stat-mechhep-thmath-ph

手性波茨模型的杨-巴克斯特方程与可积准费米子

The Yang-Baxter Equation for the Chiral Potts Model and Integrable Parafermions

Department of Physics, University of Oslo（奥斯陆大学物理系）

从手性波茨模型的星-三角和星-星关系构造出具有三个谱参数的杨-巴克斯特方程，推广了可积边模型与顶点模型的统一。

2026-08-18cond-mat.stat-mechhep-thmath-ph