q-Deformed Anisotropic Superexchange Interaction, Frustration and GL_{pq}(2)

Abstract

We study a suitable q-deformed version of the Moriya's superexchange interaction theory by means of its underlying quantum group structure. We show that the one-dimensional chain case is associated with the non-standard quantum group $GL_{pq}(2) $, evidencing the integrability structure of the system. This biparametric deformation of $GL(2,{\bf C}) $ arise as a twisting of $GL_{q}(2) $ and it match exactly the local rotation appearing in the Shekhtman's work \cite{Sh}. This allow us to express the frustration condition in terms of this twisting, also showing that effect of the Moriya's vector amounts to a twisting of the boundary condition.