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We present a nested algebraic Bethe ansatz for a one dimensional open spin chain whose boundary quantum spaces are irreducible $\mathfrak{so}_{2n}$- or $\mathfrak{sp}_{2n}$-representations and the monodromy matrix satisfies the defining…

Mathematical Physics · Physics 2019-09-27 Allan Gerrard , Niall MacKay , Vidas Regelskis

The procedure for obtaining integrable open spin chain Hamiltonians via reflection matrices is explicitly carried out for some three-state vertex models. We have considered the 19-vertex models of Zamolodchikov-Fateev and Izergin-Korepin,…

Exactly Solvable and Integrable Systems · Physics 2014-11-18 E. C. Fireman , A. Lima-Santos , W. Utiel

The encoding of all possible sets of Bethe equations for a spin chain with SU(N|M) symmetry into a QQ-system calls for an expression of spin chain overlaps entirely in terms of Q-functions. We take a significant step towards deriving such a…

High Energy Physics - Theory · Physics 2023-02-22 Charlotte Kristjansen , Dennis Müller , Konstantin Zarembo

Based on the inhomogeneous T-Q relation and the associated Bethe Ansatz equations obtained via the off-diagonal Bethe Ansatz, we construct the Bethe-type eigenstates of the SU(2)-invariant spin-s chain with generic non-diagonal boundaries…

Mathematical Physics · Physics 2016-08-18 Lijun Yang , Xin Zhang , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

The 1D Heisenberg spin chain with anisotropy of the XXZ type is analyzed in terms of the symmetry given by the quantum Galilei group Gamma_q(1). We show that the magnon excitations and the s=1/2, n-magnon bound states are determined by the…

High Energy Physics - Theory · Physics 2009-10-22 F. Bonechi , E. Celeghini , R. Giachetti , E. Sorace , M. Tarlini

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 find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for $U_q(sl(2))$ symmetry of the Hamiltonian.…

High Energy Physics - Theory · Physics 2009-10-31 V. Fridkin , Yu. Stroganov , D. Zagier

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

We construct the family of spin chain Hamiltonians, which have affine quantum group symmetry. Their eigenvalues coincide with the eigenvalues of the usual spin chain Hamiltonians, but have the degeneracy of levels, corresponding to affine…

Condensed Matter · Physics 2008-02-03 A. Avakyan , T. Hakobyan , A. Sedrakyan

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 construct the family of spin chain Hamiltonians, which have affine $U_q g$ guantum group symmetry. Their eigenvalues coincides with the eigenvalues of the usual spin chain Hamiltonians which have non-affine $U_q g_0$ quantum group…

High Energy Physics - Theory · Physics 2007-05-23 T. Hakobyan , A. Sedrakyan

Extensive numerical analysis of the eigenspectra of the $SU_q(N)$ invariant Perk-Schultz Hamiltonian shows some simple regularities for a significant part of the eigenspectrum. Inspired by those results we have found two set of solutions of…

Statistical Mechanics · Physics 2010-04-07 F. C. Alcaraz , Yu. G. Stroganov

We find closed formulas for the overlaps of Bethe eigenstates of $\mathfrak{gl}(N)$ symmetric spin chains and integrable boundary states. We derive the general overlap formulas for $\mathfrak{gl}(M)\oplus\mathfrak{gl}(N-M)$ symmetric…

High Energy Physics - Theory · Physics 2023-12-21 Tamas Gombor

We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint [J. Phys. A 37 (2004), 433-440, arXiv:hep-th/0304092]. The…

High Energy Physics - Theory · Physics 2023-07-18 Dmitry Chernyak , Azat M. Gainutdinov , Jesper Lykke Jacobsen , Hubert Saleur

We consider the Temperley-Lieb (TL) open quantum spin chain with "free" boundary conditions associated with the spin-$s$ representation of quantum-deformed $sl(2)$. We construct the transfer matrix, and determine its eigenvalues and the…

Mathematical Physics · Physics 2016-10-04 Rafael I. Nepomechie , Rodrigo A. Pimenta

Quantum invariants of the orbit dependent pairing problem are identified in the limit where the orbits become degenerate. These quantum invariants are simultaneously diagonalized with the help of the Bethe ansatz method and a symmetry in…

Mathematical Physics · Physics 2008-06-12 Y. Pehlivan

We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ symmetry is broken. With the help of the fusion…

Mathematical Physics · Physics 2023-04-20 Guang-Liang Li , Junpeng Cao , Xiao-Tian Xu , Kun Hao , Pei Sun , Tao Yang , Wen-Li Yang

We consider lambda and anisotropic deformations of the SU(2) principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ…

High Energy Physics - Theory · Physics 2018-09-26 Calan Appadu , Timothy J. Hollowood , Dafydd Price , Daniel C. Thompson

Q-systems provide an efficient way of solving Bethe equations. We formulate here Q-systems for both the isotropic and anisotropic open Heisenberg quantum spin-1/2 chains with diagonal boundary magnetic fields. We check these Q-systems using…

High Energy Physics - Theory · Physics 2020-08-26 Rafael I. Nepomechie

We study the quantum integrable spin chain model associated with the twisted $D_2^{(2)}$ algebra (or simply the $D_2^{(2)}$ model) under generic open boundary conditions. The Hamiltonian of this model can be factorized into the sum of two…

Mathematical Physics · Physics 2025-05-19 Pengcheng Lu , Junpeng Cao , Wen-Li Yang , Ian Marquette , Yao-Zhong Zhang