Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1406.5757 · Journal of Statistical Mechanics Theory and Experiment

Algebraic Bethe ansatz for 19-vertex models with upper triangularK-matrices

Rodrigo A. Pimenta, A. Lima-Santos

Published Nov 6, 2014• 2 citations
arXivHTMLPDF

Abstract

By means of an algebraic Bethe ansatz approach, we study the Zamolodchikov–Fateev and Izergin–Korepin vertex models with non-diagonal boundaries, characterized by reflection matrices with an upper triangular form. Generalized Bethe vectors are used to diagonalize the associated transfer matrix. The eigenvalues as well as the Bethe equations are presented.

DOI
10.1088/1742-5468/2014/11/p11007

Related papers

Algebraic Bethe ansatz for the six vertex model with upper triangularK-matrices

Rodrigo A. Pimenta, A Lima-Santos

We consider a formulation of the algebraic Bethe ansatz for the six vertex model with non-diagonal open boundaries. Specifically, we study the case where both left and right K -matrices have an upper triangular form. We show that the main difficulty entailed by those forms of the K -matrices is the construction of the excited states. However, it is possible to treat this problem with the aid of an auxiliary transfer matrix and by means of a generalized creation operator.

arXiv:1308.4446•Journal of Physics A Mathematical and Theoretical•Oct 24, 2013•24 citations

Bethe Ansatze for Nineteen-vertex Models

A. Lima-Santos

The nineteen-vertex models of Zamolodchikov-Fateev, Izergin-Korepin and the supersymmetric osp(1|2) with periodic boundary conditions are studied. We find the spectrum of these quantum spin chains using the Coordinate Bethe Ansatz. The approche is a suitable parametrization of their wavefunctions. We also applied the Algebraic Bethe Ansatz in order to obtain the eigenvalues and eigenvectors of the corresponding transfer matrices.

•Jul 29, 1998•4 citations

Bethe ansätze for 19-vertex models

A. Lima-Santos

The 19-vertex models of Zalomodchikov-Fateev, Izergin-Korepin and the supersymmetric with periodic boundary conditions are studied. We find the spectrum of these quantum spin chains using the coordinate Bethe ansatz. The approach is a suitable parametrization of their wavefunctions. We also applied the algebraic Bethe ansatz in order to obtain the eigenvalues and eigenvectors of the corresponding transfer matrices.

arXiv:hep-th/9807219•Journal of Physics A Mathematical and General•Jan 1, 1999•25 citations

The nineteen-vertex model and alternating sign matrices

Christian Hagendorf

It is shown that the transfer matrix of the inhomogeneous nineteen-vertex model with certain diagonal twisted boundary conditions possesses a simple eigenvalue. This is achieved through the identification of a simple and completely explicit solution of its Bethe equations. The corresponding eigenvector is computed by means of the algebraic Bethe ansatz and both a simple component and its square norm are expressed in terms of the Izergin–Korepin determinant. In the homogeneous limit, the vector coincides with a supersymmetry singlet of the twisted spin-one XXZ chain. It is shown that in a natural polynomial normalisation scheme its square norm and the simple component coincide with generating functions for weighted enumeration of alternating sign matrices.

arXiv:1405.4726•Journal of Statistical Mechanics Theory and Experiment•Jan 19, 2015•10 citations

Algebraic Bethe ansatz for 19-vertex models with reflection conditions

Wagner Utiel

In this work we solve the 19-vertex models with the use of algebraic Bethe ansatz for diagonal reflection matrices (Sklyanin K -matrices). The eigenvectors, eigenvalues and Bethe equations are given in a general form. Quantum spin chains of spin one derived from the 19-vertex models were also discussed.

Journal of Physics A Mathematical and General•Aug 27, 2003•1 citation

Algebraic Bethe Ansatz Solution to C N Vertex Model with Open Boundary Conditions

Guang-Liang Li, Kangjie Shi, Rui‐Hong Yue

We present three diagonal reflecting matrices for the C N vertex model with open boundary conditions and exactly solve the model by using the algebraic Bethe ansatz. The eigenvector is constructed and the eigenvalue and the associated Bethe equations are achieved. All the unwanted terms are cancelled out by three kinds of identities.

Communications in Theoretical Physics•Jul 1, 2005•6 citations
By means of an algebraic Bethe ansatz approach, we study the Zamolodchikov–Fateev and Izergin–Korepin vertex models with non-diagonal boundaries, characterized by reflection matrices with an upper triangular form. Generalized Bethe vectors are used to diagonalize the associated transfer matrix. The eigenvalues as well as the Bethe equations are presented.
It is shown that the transfer matrix of the inhomogeneous nineteen-vertex model with certain diagonal twisted boundary conditions possesses a simple eigenvalue. This is achieved through the identification of a simple and completely explicit solution of its Bethe equations. The corresponding eigenvector is computed by means of the algebraic Bethe ansatz and both a simple component and its square norm are expressed in terms of the Izergin–Korepin determinant. In the homogeneous limit, the vector coincides with a supersymmetry singlet of the twisted spin-one XXZ chain. It is shown that in a natural polynomial normalisation scheme its square norm and the simple component coincide with generating functions for weighted enumeration of alternating sign matrices.