Large scale excitations for multicomponent order parameter in the planar magnetic with spin s=1
In this work we use Heisenberg magnetic model with biquadratic exchange. In the case of spin s=1 quadrupole operators together with spin operators form algebra su(3). By means of mean field approximation we obtain motion equations for so called magnetic coordinates. Remarkably, that the motion equations are integrable in dimension one. Some of magnetic coordinates serve as a multicomponent order parameter. The construction is easily generalized to the planar case.
Examining geometry and topology of coadjoint orbits of complexified algebra sl(3,C) we find the proper parameterization of all possible orbits (by means of stereographic projection) that gives variables convenient to calculate topological charge and free energy. In terms of new variables we solve the problem of minimization of free energy and obtain topologicaly stable solutions which are expansion of Belavin-Polyakov soliton in the case of group SU(3). It appears that the solutions which we call topological excitations can arise spontaneously and cause destruction of biquadratic order.
Joint work with Petro Holod (National University of "Kyiv-Mohyla Academy" and Bogolyubov Institute for Theoretical Physics, Kyiv, Ukraine).