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:nlin/0504060 · International Journal of Modern Physics B

GAUDIN MAGNET WITH IMPURITY AND ITS GENERALIZED KNIZHNIK–ZAMOLODCHIKOV EQUATION

A. LIMA-SANTOS, WAGNER UTIEL

Published Jun 8, 2006• 7 citations
arXivHTMLPDF

Abstract

This work is concerned with the formulation of the boundary quantum inverse scattering method for the xxz Gaudin magnet coupled to boundary impurities with arbitrary exchange constants. The Gaudin magnet is diagonalized by taking a quasi-classical limit of the inhomogeneous lattice. Using the method proposed by Babujian, the integral representation for the solution of the Knizhnik–Zamolodchikov equation is explictly constructed and its rational limit discussed.

DOI
10.1142/s0217979206034595

Related papers

Gaudin magnet with boundary and generalized Knizhnik-Zamolodchikov equation

Kazuhiro Hikami

We consider the boundary quantum inverse scattering method established by Sklyanin (1988). The Gaudin magnet with boundary is diagonalized by taking a quasi-classical limit of the inhomogeneous lattice. Using the method proposed by Babujian (1993), the integral representation for the solution of the B-type Knizhnik-Zamolodchikov equation is explicitly constructed.

Journal of Physics A Mathematical and General•Sep 7, 1995•44 citations

osp(1|2) off-shell Bethe ansatz equation with boundary terms

A Lima-Santos

This work is concerned with the quasi-classical limit of the boundary quantum inverse scattering method for the osp(1|2) vertex model with diagonal K matrices. In this limit Gaudin's Hamiltonians with boundary terms are presented and diagonalized. Moreover, integral representations for correlation functions are realized to be solutions of the trigonometric Knizhnik–Zamolodchikov equations.

arXiv:nlin/0610054•Journal of Statistical Mechanics Theory and Experiment•Dec 22, 2006•2 citations

Thesl(2|1)(2)Gaudin magnet with diagonal boundary terms

A. Lima-Santos

This work is concerned with the quasi-classical limit of the boundary quantum inverse scattering method for the twisted sl (2|1) (2) vertex model with diagonal K -matrices. In this limit Gaudin’s Hamiltonians with diagonal boundary terms are presented and diagonalized.

Journal of Statistical Mechanics Theory and Experiment•Jul 16, 2009•7 citations

Off-Shell Bethe Ansatz Equation for Gaudin Magnets and Solutions of Knizhnik-Zamolodchikov Equations

H. Babujian, Flume, R. (Bonn Univ. (Germany). Physikalisches Inst.), Bonn Univ. (Germany). Physikalisches Inst.

We generalize the previously established connection between the off-shell Bethe ansatz equation for inhomogeneous SU(2) lattice vertex models in the quasiclassical limit and the solutions of the SU(2) Knizhnik-Zamolodchikov equations to the case of arbitrary simple Lie algebras. (orig.)

•Jan 1, 1993•95 citations

Boundary transfer matrices and boundary quantum KZ equations

Bart Vlaar

A simple relation between inhomogeneous transfer matrices and boundary quantum Knizhnik-Zamolodchikov (KZ) equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus, the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin’s boundary transfer matrices by merely imposing appropriate reflection equations, in particular without using the conditions of crossing symmetry and unitarity of the R-matrix.

arXiv:1408.3364•Journal of Mathematical Physics•Jul 1, 2015•15 citations

The openXXZchain with boundary impurities

Shu Chen, Yupeng Wang, Fu‐Cho Pu

We propose an integrable open XXZ chain coupled to the boundary impurities with arbitrary exchange constants. The Bethe ansatz equation and eigenvalues are obtained by using the quantum inverse scattering method. The ground-state properties are discussed by solving the Bethe equation in some special cases. In addition, we present an approach for constructing the reflecting matrix K which produces the boundary term coupled to impurities.

Journal of Physics A Mathematical and General•May 22, 1998•9 citations
This work is concerned with the formulation of the boundary quantum inverse scattering method for the xxz Gaudin magnet coupled to boundary impurities with arbitrary exchange constants. The Gaudin magnet is diagonalized by taking a quasi-classical limit of the inhomogeneous lattice. Using the method proposed by Babujian, the integral representation for the solution of the Knizhnik–Zamolodchikov equation is explictly constructed and its rational limit discussed.
A simple relation between inhomogeneous transfer matrices and boundary quantum Knizhnik-Zamolodchikov (KZ) equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus, the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin’s boundary transfer matrices by merely imposing appropriate reflection equations, in particular without using the conditions of crossing symmetry and unitarity of the R-matrix.