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Related papers: Towards the solution of an integrable $D_2^{(2)}$ …

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We formulate $Q$-systems for the closed XXZ, open XXX and open quantum-group-invariant XXZ quantum spin chains. Polynomial solutions of these $Q$-systems can be found efficiently, which in turn lead directly to the admissible solutions of…

High Energy Physics - Theory · Physics 2021-05-19 Zoltán Bajnok , Etienne Granet , Jesper Lykke Jacobsen , Rafael I. Nepomechie

With the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the $XXX$ spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer…

Mathematical Physics · Physics 2015-06-16 Junpeng Cao , Wenli Yang , Kangjie Shi , Yupeng Wang

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

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 present a supermatrix realisation of q-deformed spinor-spinor and spinor-vector R-matrices. These R-matrices are then used to construct transfer matrices for $U_{q^2}(\mathfrak{so}_{2n+1})$- and $U_{q}(\mathfrak{so}_{2n+2})$-symmetric…

Exactly Solvable and Integrable Systems · Physics 2021-11-04 Vidas Regelskis

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

We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction, also known as zigzag spin chains. We completely classify the integrability and non-integrability of the above class of spin…

Statistical Mechanics · Physics 2026-04-13 Naoto Shiraishi

We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for this model can be formulated in terms of functional equations obtained by separation of…

Statistical Mechanics · Physics 2011-03-07 Holger Frahm , Jan H. Grelik , Alexander Seel , Tobias Wirth

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

We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of such boundaries is associated with non-diagonal twist matrices. For such models there are no trivial reference states upon…

High Energy Physics - Theory · Physics 2016-09-06 C. M. Yung , M. T. Batchelor

The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…

Mathematical Physics · Physics 2015-06-09 Yupeng Wang , Wen-Li Yang , Junpeng Cao , Kangjie Shi

In this paper we investigate complex solutions of the Bethe equations in the two-particle sector both for arbitrary finite number of sites and for the thermodynamic limit . We find the number of complex solutions (strings) and compare it…

High Energy Physics - Theory · Physics 2014-11-18 A. Ilakovac , M. Kolanovic , S. Pallua , P. Prester

We study the exact solutions of quantum integrable model associated with the $C_n$ Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method.…

Mathematical Physics · Physics 2021-02-25 Guang-Liang Li , Panpan Xue , Pei Sun , Hulin Yang , Xiaotian Xu , Junpeng Cao , Tao Yang , Wen-Li Yang

The Nested Bethe Ansatz is generalized to open and independent boundary conditions depending on two continuous and two discrete free parameters. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex models and…

High Energy Physics - Theory · Physics 2009-10-28 H. J. de Vega , A. González--Ruiz

The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are…

Mathematical Physics · Physics 2015-06-18 Xin Zhang , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

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

In 2005, Berenstein and Vazquez determined an open spin chain Hamiltonian describing the one-loop anomalous dimensions of determinant-like operators corresponding to open strings attached to Y=0 maximal giant gravitons. We construct the…

High Energy Physics - Theory · Physics 2015-05-30 Rafael I. Nepomechie

We have applied the analytical Bethe ansatz approach in order to solve the $Osp(1|2n)$ invariant magnet. By using the Bethe ansatz equations we have calculated the ground state energy and the low-lying dispersion relation. The finite size…

High Energy Physics - Theory · Physics 2016-09-06 M. J. Martins

In this paper we study the spectrum of the spin-1 Temperley-Lieb spin chain with integrable open boundary conditions. We obtain the eigenvalue expressions as well as its associated Bethe ansatz equations by means of the coordinate Bethe…

Exactly Solvable and Integrable Systems · Physics 2013-06-25 G. A. P. Ribeiro , A. Lima-Santos

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