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


SIGMA 7 (2011), 012, 22 pages      arXiv:1011.0660      http://dx.doi.org/10.3842/SIGMA.2011.012
Contribution to the Proceedings of the International Workshop “Recent Advances in Quantum Integrable Systems”

Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End

Ghali Filali a and Nikolai Kitanine b
a) Université de Cergy-Pontoise, LPTM UMR 8089 du CNRS, 2 av. Adolphe Chauvin, 95302 Cergy-Pontoise, France
b) Université de Bourgogne, Institut de Mathématiques de Bourgogne UMR 5584 du CNRS, 9 av. Alain Savary - B.P. 47 870, 21078 Dijon, France

Received October 28, 2010, in final form January 11, 2011; Published online January 27, 2011

Abstract
In this paper we consider two a priori very different problems: construction of the eigenstates of the spin chains with non parallel boundary magnetic fields and computation of the partition function for the trigonometric solid-on-solid (SOS) model with one reflecting end and domain wall boundary conditions. We show that these two problems are related through a gauge transformation (so-called vertex-face transformation) and can be solved using the same dynamical reflection algebras.

Key words: algebraic Bethe ansatz; spin chains; dynamical reflection algebra; SOS models.

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