q-Deformed Anisotropic Superexchange Interaction, Frustration and GLpq(2)

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 GLpq(2), evidencing the integrability structure of the system. This biparametric deformation of GL(2; C) arise as a twisting of GLq(2) and it match exactly the local rotation appearing in the Shekhtman's work.1 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.