English
Related papers

Related papers: Factorization identities and algebraic Bethe ansat…

200 papers

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

The full set of polynomial solutions of the nested Bethe Ansatz is constructed for the case of A_2 rational spin chain. The structure and properties of these associated solutions are more various then in the case of usual XXX (A_1) spin…

High Energy Physics - Theory · Physics 2009-10-31 G. P. Pronko , Yu. G. Stroganov

New identities on traces of representations of the Hecke algebra on the spaces of paths on graphs are presented. These identities are relevant in the computation of partition functions with fixed boundary conditions and of two-point…

q-alg · Mathematics 2009-10-30 S. Loesch , Y-K Zhou , J-B Zuber

We study the diagonalization problem of certain Hofstadter-type models through the algebraic Bethe ansatz equation by the algebraic geometry method. When the spectral variables lie on a rational curve, we obtain the complete and explicit…

Condensed Matter · Physics 2008-11-26 Shao-shiung Lin , Shi-shyr Roan

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

We consider an $XYZ$ spin chain within the framework of the generalized algebraic Bethe ansatz. We study form factors of local operators corresponding to the singlet states in the limit of free fermions. We obtain explicit representations…

Mathematical Physics · Physics 2023-09-13 G. Kulkarni , N. A. Slavnov

The asymmetric exclusion process on a ring in one-dimension is considered with a single defect particle. The steady state has previously been solved by a matrix product method. Here we use the Bethe ansatz to solve exactly for the long time…

Statistical Mechanics · Physics 2009-10-31 B. Derrida , M. R. Evans

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

In this paper, we consider the quantum XYZ open spin-1/2 chain with boundary fields. We focus on the particular case in which the six boundary parameters are related by a single constraint enabling us to describe part of the spectrum by…

Mathematical Physics · Physics 2025-07-30 G. Niccoli , V. Terras

We use the exact determinantal representation derived by Kitanine, Maillet, and Terras for matrix elements of local spin operators between Bethe wave functions of the one-dimensional s=1/2 Heisenberg model to calculate and numerically…

Strongly Correlated Electrons · Physics 2009-11-07 Daniel Biegel , Michael Karbach , Gerhard Muller

We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of…

Mathematical Physics · Physics 2017-05-24 Azat M. Gainutdinov , Wenrui Hao , Rafael I. Nepomechie , Andrew J. Sommese

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

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

We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…

Quantum Algebra · Mathematics 2014-02-26 Óscar Cortadellas , Javier López Peña , Gabriel Navarro

We diagonalize infinitely many commuting operators $T_B(z)$. We call these operators $T_B(z)$ the boundary transfer matrix associated with the quantum group and the elliptic quantum group. The boundary transfer matrix is related to the…

Exactly Solvable and Integrable Systems · Physics 2015-05-27 Takeo Kojima

The spin-1/2 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the…

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

Conditions of integrability of general zero range chipping models with factorized steady state, which were proposed in [Evans, Majumdar, Zia 2004 J. Phys. A 37 L275], are examined. We find a three-parametric family of hopping probabilities…

Mathematical Physics · Physics 2013-11-06 A. M. Povolotsky

We use the algebraic Bethe ansatz to obtain the eigenvalues and eigenvectors of the spin-1 Temperley-Lieb open quantum chain with "free" boundary conditions. We exploit the associated reflection algebra in order to prove the off-shell…

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

The second reference state of the open XXZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz. In the quasi-classical…

High Energy Physics - Theory · Physics 2010-10-27 Wen-Li Yang , Yao-Zhong Zhang

It is shown that solutions of the Bethe ansatz equations for the inhomogeneous arbitrary spin XXX or XXZ model satisfy certain identites which generalize those, recently obtained by K.Fabricius and B.M.McCoy, for solutions of the Bethe…

Mathematical Physics · Physics 2007-05-23 V. Tarasov