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arXiv:1011.0660 · Symmetry Integrability and Geometry Methods and Applications

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

Ghali Filali

Published Jan 27, 2011• 31 citations
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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.

DOI
10.3842/sigma.2011.012

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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.
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In this paper we compute the most general non-diagonal reflection matrices of the RSOS/SOS models and the hard hexagon model using the boundary Yang-Baxter equations. We find a new one-parameter family of the reflection matrices for the RSOS model in addition to the previous result obtained in Ahn C and Koo W M 1996 Nucl. Phys. B 468 [FS] 461. We also find three classes of the reflection matrices for the SOS model, which has one or two free parameters. For the hard-hexagon model which can be mapped to the RSOS(5) model by folding four RSOS heights into two, the solutions can be obtained similarly with a main difference in the boundary unitarity conditions. Due to this, the reflection matrices can have two free parameters. We show that these extra terms can be identified with the `decorated' solutions. We also generalize the hard hexagon model by `folding' the RSOS heights of the general RSOS( p ) model and show that they satisfy the integrability conditions such as the Yang-Baxter and boundary Yang-Baxter equations. These models can be solved using the results for the RSOS models.