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In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz…

Mathematical Physics · Physics 2012-06-28 S. Belliard , E. Ragoucy

A general method is proposed for constructing the Bethe ansatz equations of integrable models without U(1) symmetry. As an example, the exact spectrum of the XXZ spin ring with M{\" o}bius like topological boundary condition is derived by…

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

We consider the finite volume mean values of current operators in integrable spin chains with local interactions, and provide an alternative derivation of the exact result found recently by the author and two collaborators. We use a certain…

Statistical Mechanics · Physics 2020-02-05 Balázs Pozsgay

We discuss the AdS/CFT duality from the perspective of integrable systems and establish a direct relationship between the dimension of single trace local operators composed of two types of scalar fields in N=4 super Yang-Mills and the…

High Energy Physics - Theory · Physics 2009-11-10 V. A. Kazakov , A. Marshakov , J. A. Minahan , K. Zarembo

We investigate the effect of introducing a boundary inhomogeneity in the transfer matrix of an integrable open quantum spin chain. We find that it is possible to construct a local Hamiltonian, and to have quantum group symmetry. The…

High Energy Physics - Theory · Physics 2021-09-01 Rafael I. Nepomechie , Ana L. Retore

We consider the Bethe ansatz solution of integrable models interacting through factorized $S$-matrices based on the central extention of the $\bf{su}(2|2)$ symmetry. The respective $\bf{su}(2|2)$ $R$-matrix is explicitly related to that of…

High Energy Physics - Theory · Physics 2008-11-26 M. J. Martins , C. S. Melo

We formulate the thermodynamic Bethe Ansatz (TBA) equations for the closed (periodic boundary conditions) $A^{(2)}_2$ quantum spin chain in an external magnetic field, in the (noncritical) regime where the anisotropy parameter $\eta$ is…

High Energy Physics - Theory · Physics 2009-10-22 Luca Mezincescu , Rafael I. Nepomechie , P. K. Townsend , A. M. Tsvelik

Every solution of the Bethe ansatz equations (BAE) is characterized by a set of quantum numbers called the Bethe quantum numbers, which are fundamental for evaluating it numerically. We rigorously derive the Bethe quantum numbers for the…

Mathematical Physics · Physics 2024-09-10 Takashi Imoto , Tetsuo Deguchi

We study the finite size scaling of the spin stiffness for the one-dimensional s=1/2 quantum antiferromagnet as a function of the anisotropy parameter Delta.Previous Bethe ansatz results allow a determination of the stiffness in the…

Strongly Correlated Electrons · Physics 2017-01-31 Nicolas Laflorencie , Sylvain Capponi , Erik S. Sorensen

We consider GL(K|M)-invariant integrable supersymmetric spin chains with twisted boundary conditions and elucidate the role of Backlund transformations in solving the difference Hirota equation for eigenvalues of their transfer matrices.…

High Energy Physics - Theory · Physics 2009-11-13 A. Zabrodin

We consider the quantum integrable spin chain models associated with the Jimbo R-matrix based on the quantum affine algebra $D^{(2)}_{n+1}$, subject to quantum-group-invariant boundary conditions parameterized by two discrete variables…

High Energy Physics - Theory · Physics 2025-12-19 Holger Frahm , Sascha Gehrmann , Rafael I. Nepomechie , Ana L. Retore

Commuting transfer matrices for linear chains of interacting non-Abelian anyons from the two-dimensional irreducible representation of the dihedral group $D_3$ (or, equivalently, the integer sector of the $su(2)_4$ spin-$1$ chain) are…

Strongly Correlated Electrons · Physics 2016-08-31 Natalia Braylovskaya , Peter E. Finch , Holger Frahm

In integrable spin chains, the spectral problem can be solved by the method of Bethe ansatz, which transforms the problem of diagonalization of the Hamiltonian into the problem of solving a set of algebraic equations named Bethe equations.…

High Energy Physics - Theory · Physics 2025-08-27 Yi-Jun He , Jue Hou , Yi-Chao Liu , Zi-Xi Tan

Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras $\hat g$, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently…

High Energy Physics - Theory · Physics 2018-12-26 Rafael I. Nepomechie , Ana L. Retore

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

We extend Sklyanin's construction of commuting open-chain transfer matrices to the SU(2|2) bulk and boundary S-matrices of AdS/CFT. Using the graded version of the S-matrices leads to a transfer matrix of particularly simple form. We also…

High Energy Physics - Theory · Physics 2014-11-18 Rajan Murgan , Rafael I. Nepomechie

In this chapter of "Review of AdS/CFT Integrability" we introduce N=4 Super Yang-Mills. We discuss the global superalagebra PSU(2,2|4) and its action on gauge invariant operators. We then discuss the computation of the correlators of…

High Energy Physics - Theory · Physics 2015-05-20 Joseph A. Minahan

The $A^{(1)}_{n-1}$ trigonometric vertex model with {\it generic non-diagonal} boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the…

High Energy Physics - Theory · Physics 2010-01-08 Wen-Li Yang , Yao-Zhong Zhang

We employ the analytic Bethe Anzats to construct eigenvalues of transfer matrices with finite-dimensional atypical representations in the auxiliary space for the putative long-range spin chain encoding anomalous dimensions of all composite…

High Energy Physics - Theory · Physics 2008-11-26 A. V. Belitsky

In this paper, we consider the parameterization of the spectra of the three-state critical Potts quantum chain with integrable twisted boundary conditions in terms of Bethe ansatz type equations. The Bethe equations are found by…

Mathematical Physics · Physics 2026-02-23 M. J. Martins