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Related papers: Switch Operators for the Six-Vertex Model

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In this paper, we consider the quantum XYZ open spin-1/2 chain with boundary fields. We focus on the particular case in which the six boundary parameters are related by a single constraint enabling us to describe part of the spectrum by…

Mathematical Physics · Physics 2025-07-30 G. Niccoli , V. Terras

We find shift operators for the Dotsenko-Fateev equation, which is a differential equation of order 3, and for the three Fuchsian differential equations of order 4, 5 and 6, respectively, which are connected with the Dotsenko-Fateev…

Classical Analysis and ODEs · Mathematics 2025-10-27 Yoshishige Haraoka , Hiroyuki Ochiai , Takeshi Sasaki , Masaaki Yoshida

We study the scaling limit of a statistical system, which is a special case of the integrable inhomogeneous six-vertex model. It possesses $U_q\big(\mathfrak{sl}(2)\big)$ invariance due to the choice of open boundary conditions imposed. An…

High Energy Physics - Theory · Physics 2024-06-05 Holger Frahm , Sascha Gehrmann , Gleb A. Kotousov

We explicitly determine all Rota-Baxter operators (of weight zero) on $sl(2,C)$ under the Cartan-Weyl basis. For the skew-symmetric operators, we give the corresponding skew-symmetric solutions of the classical Yang-Baxter equation in…

Mathematical Physics · Physics 2015-06-17 Jun Pei , Chengming Bai , Li Guo

Correlation functions of the six and nineteen vertex models on an N \times N lattice with domain wall boundary conditions are studied. The general expression of the boundary correlation functions is obtained for the six vertex model by use…

Mathematical Physics · Physics 2011-08-02 Kohei Motegi

We address the question of the dependence of the bulk free energy on boundary conditions for the six vertex model. Here we compare the bulk free energy for periodic and domain wall boundary conditions. Using a determinant representation for…

Statistical Mechanics · Physics 2009-10-31 V. Korepin , P. Zinn-Justin

We construct embeddings of boundary algebras B into ZF algebras A. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for B and without for A), this connection allows to…

Quantum Algebra · Mathematics 2007-05-23 E. Ragoucy

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in \cite{deLeeuw:2019zsi}. We provide details on how to find all non-difference…

Mathematical Physics · Physics 2021-11-05 Marius de Leeuw , Chiara Paletta , Anton Pribytok , Ana L. Retore , Paul Ryan

We develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the…

Mathematical Physics · Physics 2011-06-13 Vladimir V. Bazhanov , Rouven Frassek , Tomasz Lukowski , Carlo Meneghelli , Matthias Staudacher

We propose a new approach to studying electrical networks interpreting the Ohm law as the operator which solves certain Local Yang-Baxter equation. Using this operator and the medial graph of the electrical network we define a vertex…

Mathematical Physics · Physics 2020-12-02 Vassily Gorbounov , Dmitry Talalaev

Starting with any R-matrix with spectral parameter, obeying the Yang-Baxter equation and a unitarity condition, we construct the corresponding infinite dimensional quantum group U_{R} in term of a deformed oscillators algebra A_R. The…

Quantum Algebra · Mathematics 2008-11-26 E. Ragoucy

We observe that the partition function of the six vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP tau function and express it as an expectation value of charged free fermions (up to an…

Mathematical Physics · Physics 2009-03-11 O Foda , M Wheeler , M Zuparic

We discuss the influence of boundary conditions on the continuum limit of the six-vertex model by deriving a variational principle for the associated height function with arbitrary fixed boundary conditions. We discuss its consequences…

Statistical Mechanics · Physics 2007-05-23 P. Zinn-Justin

In this work we obtain hierarchies of partial differential equations describing on-shell scalar products for two types of six-vertex models. More precisely, six-vertex models with two different diagonal boundary conditions are considered:…

Mathematical Physics · Physics 2015-10-06 W. Galleas , J. Lamers

The boundary-value problem on semi-axis for one class operator-differential equations of the fourth order, the main part of which has the multiple characteristic is investigated in this paper in Sobolev type weighted space. Correctness and…

Functional Analysis · Mathematics 2011-07-27 A. R. Aliev

In this paper, we explain a connection between a family of free-fermionic six-vertex models and a discrete time evolution operator on one-dimensional Fermionic Fock space. The family of ice models generalize those with domain wall boundary,…

Combinatorics · Mathematics 2016-06-02 Ben Brubaker , Andrew Schultz

We discuss homogeneous Yang-Baxter deformations of integrable sigma models in terms of twist operators. We show that the twist operators behave as the classical analogue of a Drinfeld twist, for all abelian and almost abelian deformations.…

High Energy Physics - Theory · Physics 2022-04-19 Stijn J. van Tongeren

We present solutions for the (constant and spectral-parameter) Yang-Baxter equations and Yang-Baxter systems arising from algebra structures and discuss about their symmetries. In the last section, we present some applications.

Quantum Algebra · Mathematics 2014-01-03 Florin F. Nichita , Bogdan P. Popovici

A generalised ladder operator is used to construct the conserved operators for any model derived from the Yang-Baxter equation. As an example, the low order conserved operators for the XYh model are calculated explicitly.

Exactly Solvable and Integrable Systems · Physics 2007-05-23 M. Takizawa , J. Links

We use a double shifted power analog of free fermion fields to introduce current operators, Hamiltonians, and vertex operators which are deformed by two families of parameters and satisfy analogous formulas to the classical case. We show…

Representation Theory · Mathematics 2025-02-19 Daniel Bump , Andrew Hardt , Travis Scrimshaw