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The one-dimensional Hubbard model with open boundary conditions is exactly solved by means of algebraic Bethe ansatz. The eigenvalue of the transfer matrix, the energy spectrum as well as the Bethe ansatz equations are obtained.

Statistical Mechanics · Physics 2009-10-31 X. -W. Guan

We diagonalize the double-row transfer matrix of the SU(N) vertex model for certain classes of non-diagonal boundary conditions. We derive explicit expressions for the corresponding eigenvectors and eigenvalues by means of the algebraic…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 W. Galleas , M. J. Martins

In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in the framework of the quantum inverse scattering method. Following the algebraic Bethe ansatz we diagonalise the introduced…

Mathematical Physics · Physics 2023-01-04 Rouven Frassek , István M. Szécsényi

The Lie superalgebra sl(r+1|s+1) admits several inequivalent choices of simple root systems. We have carried out analytic Bethe ansatz for any simple root systems of sl(r+1|s+1). We present transfer matrix eigenvalue formulae in dressed…

Mathematical Physics · Physics 2009-12-15 Zengo Tsuboi

From the point of view of the Young superdiagrm method, an analytic Bethe ansatz is carried out for Lie superalgebra sl(r+1|s+1). For the transfer matrix eigenvalue formulae in dressed vacuum form, we present some expressions, which are…

Mathematical Physics · Physics 2009-12-15 Zengo Tsuboi

The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA into unitary form, for its direct…

As is well known, the type 1 Lie superalgebra sl(r+1|s+1) admits a one parameter family of finite dimensional irreducible representations. We have carried out an analytic Bethe ansatz related to this family of representations. We present…

Mathematical Physics · Physics 2009-12-15 Zengo Tsuboi

We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes…

Mathematical Physics · Physics 2013-11-25 Samuel Belliard , Nicolas Crampé

We extend Sklyanin's method of separation of variables to quantum integrable models associated to elliptic curves. After reviewing the differential case, the elliptic Gaudin model studied by Enriquez, Feigin and Rubtsov, we consider the…

Quantum Algebra · Mathematics 2016-09-07 Giovanni Felder , Anke Schorr

We show how any integrable 2D QFT enjoys the existence of infinitely many non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry algebra. These charges are generated by quantum monodromy operators and provide a…

High Energy Physics - Theory · Physics 2011-07-19 C. Destri , H. J. de Vega

Eigenvalues of the commuting family of transfer matrices are expected to obey the $T$-system, a set of functional relation, proposed recently. Here we obtain the solution to the $T$-system for $C^{(1)}_2$ vertex models. They are compatible…

High Energy Physics - Theory · Physics 2009-10-22 Atsuo Kuniba

We demonstrate for the six vertex and XXZ model parameterized by $\Delta=-(q+q^{-1})/2\neq \pm 1$ that when q^{2N}=1 for integer $N\geq 2$ the Bethe's ansatz equations determine only the eigenvectors which are the highest weights of the…

Statistical Mechanics · Physics 2011-07-19 Klaus Fabricius , Barry M. McCoy

The $Z_n$ elliptic Gaudin model with integrable boundaries specified by generic non-diagonal K-matrices with $n+1$ free boundary parameters is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe…

High Energy Physics - Theory · Physics 2008-11-26 W. -L. Yang , R. Sasaki , Y. -Z. Zhang

A quantum algebra invariant integrable closed spin 1 chain is introduced and analysed in detail. The Bethe ansatz equations as well as the energy eigenvalues of the model are obtained. The highest weight property of the Bethe vectors with…

solv-int · Physics 2015-06-26 Jon Links , Angela Foerster , Michael Karowski

We consider open XXX spins chain with two general boundary matrices submitted to one constraint, which is equivalent to the possibility to put the two matrices in a triangular form. We construct Bethe vectors from a generalized algebraic…

Mathematical Physics · Physics 2015-06-11 S. Belliard , N. Crampe , E. Ragoucy

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…

Mathematical Physics · Physics 2014-11-07 R. A. Pimenta , A. Lima-Santos

We consider the integrable open XX quantum spin chain with nondiagonal boundary terms. We derive an exact inversion identity, using which we obtain the eigenvalues of the transfer matrix and the Bethe Ansatz equations. For generic values of…

High Energy Physics - Theory · Physics 2008-11-26 Rafael I. Nepomechie

The formulation and resolution of integrable lattice statistical models in a quantum group covariant way is the subject of this review. The Bethe Ansatz turns to be remarkably useful to implement quantum group symmetries and to provide…

High Energy Physics - Theory · Physics 2008-02-03 H. J. de Vega

An analytic Bethe ansatz is carried out related to the Lie superalgebra osp(1|2s). We present an eigenvalue formula of a transfer matrix in dressed vacuum form (DVF) labeled by a Young (super) diagram. Remarkable duality among DVFs is…

Mathematical Physics · Physics 2010-01-05 Zengo Tsuboi

This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of…

solv-int · Physics 2009-10-30 M. J. Martins , P. B. Ramos