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Related papers: Nested Bethe ansatz for `all' open spin chains wit…

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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

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

Using the algebraic Bethe ansatz, we derive a matrix product representation of the exact Bethe-ansatz states of the six-vertex Heisenberg chain (either XXX or XXZ and spin-$\frac{1}{2}$) with open boundary conditions. In this…

Quantum Physics · Physics 2017-07-14 Zhongtao Mei , C. J. Bolech

We derive the Bethe Ansatz Equations on the half line for particles interacting through factorized $S$-matrices invariant relative to the centrally extended $su(2|2)$ Lie superalgebra and $su(1|2)$ open boundaries. These equations may be of…

High Energy Physics - Theory · Physics 2009-08-03 W. Galleas

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 paper we apply the nested algebraic Bethe ansatz to compute the eigenvalues and the Bethe equations of the transfer matrix of the new integrable Lindbladian found in [1]. We show that it can be written as an integrable spin chain…

Statistical Mechanics · Physics 2022-07-29 Marius de Leeuw , Chiara Paletta

We propose an expression for the eigenvalues of the transfer matrix for the $U_q(B_n)$-invariant open quantum spin chain associated with the fundamental representation of $A^{(2)}_{2n}$. By assumption, the Bethe Ansatz equations are…

High Energy Physics - Theory · Physics 2015-06-26 Simone Artz , Luca Mezincescu , Rafael I. Nepomechie

A system of U(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz. The highest weight property of the solutions is proved and some examples of solutions are calculated explicitly. (Part II of…

High Energy Physics - Theory · Physics 2009-10-30 H. Babujian , M. Karowski , A. Zapletal

We construct the coordinate Bethe ansatz for all eigenstates of the open spin-$\frac12$ XXZ chain that fulfill the phantom roots criterion (PRC). Under the PRC, the Hilbert space splits into two invariant subspaces and there are two sets of…

Statistical Mechanics · Physics 2022-02-01 Xin Zhang , Andreas Kluemper , Vladislav Popkov

We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider…

High Energy Physics - Theory · Physics 2008-11-26 Rajan Murgan

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

We study quantum Uq(gl(N)) integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the right and left universal off-shell nested Bethe vectors. It is shown that these formulas can be related by…

Mathematical Physics · Physics 2015-06-17 S. Pakuliak , E. Ragoucy , N. A. Slavnov

We propose a Bethe-Ansatz-type solution of the open spin-1/2 integrable XXZ quantum spin chain with general integrable boundary terms and bulk anisotropy values i \pi/(p+1), where p is a positive integer. All six boundary parameters are…

High Energy Physics - Theory · Physics 2011-02-16 Rajan Murgan , Rafael I. Nepomechie , Chi Shi

We study a one-dimensional model of free fermions with $\mathfrak{gl}(1|1)$ supersymmetry and demonstrate how non-diagonal boundary conditions can be incorporated into the framework of the graded Quantum Inverse Scattering Method (gQISM) by…

Statistical Mechanics · Physics 2010-01-06 André M. Grabinski , Holger Frahm

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

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

The spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment is investigated within a modified algebraic Bethe ansatz framework. We consider in this work the most general boundaries allowed by integrability. The…

Mathematical Physics · Physics 2015-04-03 Samuel Belliard , Rodrigo A. Pimenta

We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class…

Mathematical Physics · Physics 2015-05-14 M. J. Martins , C. S. Melo

We briefly review Bethe Ansatz solutions of the integrable open spin-1/2 XXZ quantum spin chain derived from functional relations obeyed by the transfer matrix at roots of unity.

High Energy Physics - Theory · Physics 2007-05-23 Rafael I. Nepomechie

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of…

Statistical Mechanics · Physics 2009-10-30 Anthony J. Bracken , Xiang-Yu Ge , Yao-Zhong Zhang , Huan-Qiang Zhou