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We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have many solutions, so we can consider a wide variety of…

Mathematical Physics · Physics 2009-11-07 J. de Gier , V. Korepin

We express $D^{(2)}_{2}$ transfer matrices as products of $A^{(1)}_{1}$ transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz.…

High Energy Physics - Theory · Physics 2021-01-20 Rafael I. Nepomechie , Ana L. Retore

The spectral properties of operators formed from generators of the q-Onsager non-Abelian infinite dimensional algebra are investigated. Using a suitable functional representation, all eigenfunctions are shown to obey a second-order…

Mathematical Physics · Physics 2009-11-11 Pascal Baseilhac

We apply the algebraic Bethe ansatz technique to compute the eigenvalues of the transfer matrix constructed from the general bound state S-matrix of the light-cone AdS5 x S5 superstring. This allows us to verify certain conjectures on the…

High Energy Physics - Theory · Physics 2009-10-20 Gleb Arutyunov , Marius de Leeuw , Ryo Suzuki , Alessandro Torrielli

We derive, using the algebraic Bethe Ansatz, a generalized Matrix Product Ansatz for the asymmetric exclusion process (ASEP) on a one-dimensional periodic lattice. In this Matrix Product Ansatz, the components of the eigenvectors of the…

Statistical Mechanics · Physics 2009-11-11 O. Golinelli , K. Mallick

The Bariev model with open boundary conditions is introduced and analysed in detail in the framework of the Quantum Inverse Scattering Method. Two classes of independent boundary reflecting $K$-matrices leading to four different types of…

Strongly Correlated Electrons · Physics 2009-10-31 A. Foerster , X. -W. Guan , J. Links , I. Roditi , H. -Q. Zhou

The eigenvalues of the elliptic N-body Ruijsenaars operator are obtained by a dynamical version of the algebraic nested Bethe ansatz method. We use a result of Felder and Varchenko, who showed how to obtain the Ruijsenaars operator as the…

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

This paper is a continuation of our previous work (solv-int/9903001). We obtain two more functional relations for the eigenvalues of the transfer matrices for the $sl(3)$ chiral Potts model at $q^2=-1$. This model, up to a modification of…

solv-int · Physics 2009-10-31 H. E. Boos , V. V. Mangazeev

The XXX Gaudin model with generic integrable boundaries specified by the most general non-diagonal K-matrices is studied by the off-diagonal Bethe ansatz method. The eigenvalues of the associated Gaudin operators and the corresponding Bethe…

Mathematical Physics · Physics 2015-03-10 Kun Hao , Junpeng Cao , Tao Yang , Wen-Li Yang

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

The algebraic Bethe Ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations.…

Strongly Correlated Electrons · Physics 2012-07-23 Valentin Murg , Vladimir E. Korepin , Frank Verstraete

The anisotropic spin-1/2 chains with arbitrary boundary fields are diagonalized with the off-diagonal Bethe ansatz method. Based on the properties of the R-matrix and the K-matrices, an operator product identity of the transfer matrix is…

Statistical Mechanics · Physics 2015-06-16 Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

The Bethe Ansatz is a method for constructing exact eigenstates of quantum-integrable spin chains. Recently, deterministic quantum algorithms, referred to as "algebraic Bethe circuits", have been developed to prepare Bethe states for the…

Quantum Physics · Physics 2025-07-29 Roberto Ruiz , Alejandro Sopena , Esperanza López , Germán Sierra , Balázs Pozsgay

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

We introduce fusion $U_q(G^{(1)}_2)$ vertex models related to fundamental representations. The eigenvalues of their row to row transfer matrices are derived through analytic Bethe ans{\"a}tze. By combining these results with our previous…

High Energy Physics - Theory · Physics 2009-10-28 Junji Suzuki

For generic values of q, all the eigenvectors of the transfer matrix of the U_q sl(2)-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA) formalism of Sklyanin. However, when q is…

Mathematical Physics · Physics 2017-05-24 Azat M. Gainutdinov , Rafael I. Nepomechie

The nested algebraic Bethe ansatz is presented for the anisotropic supersymmetric $U$ model maintaining quantum supersymmetry. The Bethe ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for…

solv-int · Physics 2009-10-31 Katrina Hibberd , Itzhak Roditi , Jon Links , Angela Foerster

We study the large time behaviour of the solution of a linear dispersive PDEs posed on a finite interval, when the prescribed boundary conditions are time periodic. We use the approach pioneered in Fokas & Lenells 2012 for nonlinear…

Analysis of PDEs · Mathematics 2022-01-25 A. S. Fokas , B. Pelloni , D. A. Smith

A novel Bethe ansatz scheme is proposed to investigate the exact physical properties of an integrable anisotropic quantum spin chain with competing interactions among the nearest, next nearest neighbor and chiral three spin couplings, where…

Mathematical Physics · Physics 2022-02-09 Wei Wang , Yi Qiao , Junpeng Cao , Wu-Ming Liu , Rong-Hua Liu

We study the ODE/IM correspondence for ODE associated to $\hat{\mathfrak g}$-valued connections, for a simply-laced Lie algebra $\mathfrak g$. We prove that subdominant solutions to the ODE defined in different fundamental representations…

Mathematical Physics · Physics 2016-06-17 Davide Masoero , Andrea Raimondo , Daniele Valeri