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Related papers: A Q-operator for open spin chains I: Baxter's TQ r…

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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 transfer matrix of the XXZ open spin-1/2 chain with general integrable boundary conditions and generic anisotropy parameter (q is not a root of unity and |q|=1) is diagonalized using the representation theory of the q-Onsager algebra.…

High Energy Physics - Theory · Physics 2015-06-26 P. Baseilhac , K. Koizumi

We study properties of transfer matrices in the sl(N) spin chain models. The transfer matrices with an infinite dimensional auxiliary space are factorized into the product of N commuting Baxter Q-operators. We consider the transfer matrices…

Exactly Solvable and Integrable Systems · Physics 2011-07-21 S. E. Derkachov , A. N. Manashov

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

A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an…

High Energy Physics - Theory · Physics 2009-10-31 J. M. Maillet , V. Terras

We extend to regular QCD the derivation of a confining $ q \bar{q}$ Bethe--Salpeter equation previously given for the simplest model of scalar QCD in which quarks are treated as spinless particles. We start from the same assumptions on the…

High Energy Physics - Phenomenology · Physics 2014-11-17 N. Brambilla , E. Montaldi , G. M. Prosperi

We present in an unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(\fn)), Y(gl(\fm|\fn)), U_{q}(gl(\fn)) or U_{q}(gl(\fm|\fn)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of…

Mathematical Physics · Physics 2015-05-13 S. Belliard , E. Ragoucy

We derive a non-linear integral equation for the Bethe-ansatz solvable open XXZ spin chain of arbitrary length describing the lowest lying state with zero magnetization. For this case we show how to combine the integral representation with…

Mathematical Physics · Physics 2009-02-19 A. Seel , T. Wirth

We consider the algebraic Bethe ansatz solution of the integrable and isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show that the corresponding K-matrices are similar to diagonal matrices with the help of suitable…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 C. S. Melo , G. A. P. Ribeiro , M. J. Martins

In this paper we introduce Baxter integral Q-operators for finite-dimensional Lie algebras gl(n+1) and so(2n+1). Whittaker functions corresponding to these algebras are eigenfunctions of the Q-operators with the eigenvalues expressed in…

Representation Theory · Mathematics 2009-11-13 A. Gerasimov , D. Lebedev , S. Oblezin

The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant…

High Energy Physics - Theory · Physics 2009-10-22 H. J. de Vega , A. González--Ruiz

The transfer matrix of the general integrable open XXZ quantum spin chain obeys certain functional relations at roots of unity. By exploiting these functional relations, we determine the Bethe Ansatz solution for the transfer matrix…

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

We introduce a category $\mathcal O$ of representations of the elliptic quantum group associated with $\mathfrak{sl}_2$ with well-behaved $q$-character theory. We derive separation of variables relations for asymptotic representations in…

Quantum Algebra · Mathematics 2017-06-26 Giovanni Felder , Huafeng Zhang

Q-operators for generalised eight vertex models associated to higher spin representations of the Sklyanin algebra are constructed by Baxter's first method and Fabricius's method, when the anisotropy parameter is rational.

Quantum Algebra · Mathematics 2019-05-22 Takashi Takebe

We derive exactly scalar products and form factors for integrable higher-spin XXZ chains through the algebraic Bethe-ansatz method. Here spin values are arbitrary and different spins can be mixed. We show the affine quantum-group symmetry,…

Statistical Mechanics · Physics 2011-07-06 Tetsuo Deguchi , Chihiro Matsui

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

The rational $Q$-system is an efficient method to solve Bethe ansatz equations for quantum integrable spin chains. We construct the rational $Q$-systems for generic Bethe ansatz equations described by an $A_{\ell-1}$ quiver, which include…

High Energy Physics - Theory · Physics 2023-03-15 Jie Gu , Yunfeng Jiang , Marcus Sperling

In this article we have discovered a close relationship between the (algebraic) Bethe Ansatz equations of the spin $s$ XXZ model of a finite size and the $q$-Sturm-Liouville problem. We have demonstrated that solutions of the Bethe Ansatz…

Mathematical Physics · Physics 2007-05-23 M. E. H. Ismail , S. S. Lin , S. S. Roan

We compute by means of the Bethe Ansatz the boundary S matrix for the open anisotropic spin-1/2 chain with diagonal boundary magnetic fields in the noncritical regime (Delta > 1). Our result, which is formulated in terms of q-gamma…

High Energy Physics - Theory · Physics 2008-11-26 Anastasia Doikou , Luca Mezincescu , Rafael I. Nepomechie

We solve for the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}_q(X_n } for $X_n = A_1,B_n,C_n$ and $D_n$. We employ a generalization of the coordinate…

Condensed Matter · Physics 2015-06-25 R. Koberle , A. Lima-Santos