Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 9 (2013), 072, 12 pages      arXiv:1309.6165      https://doi.org/10.3842/SIGMA.2013.072

Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz

Samuel Belliard a, b and Nicolas Crampé a, b
a) Laboratoire Charles Coulomb L2C, UMR 5221, CNRS, F-34095 Montpellier, France
b) Laboratoire Charles Coulomb L2C, UMR 5221, Université Montpellier 2, F-34095 Montpellier, France

Received September 29, 2013, in final form November 19, 2013; Published online November 22, 2013

Abstract
We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.

Key words: algebraic Bethe ansatz; integrable spin chain; boundary conditions.

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