Casimir-energy-induced confinement and deconfinement of spinons in a two-dimensional anisotropic nonlinearσmodel

We consider a nonusual two-dimensional anisotropic nonlinear σ model. This model supports topological excitations (Skyrmions), which the configurations, at the classical level, resemble noninteracting vortex and antivortex defects. These vortices are spin-$1∕2$ pseudoparticles (spinons). Quantization of these defects breaks the conformal invariance of the model, leading to an effective potential of interaction between the spinons that form the Skyrmion. The nature of this interaction depends on the anisotropy parameter λ and is attractive for -1<λ<0 and repulsive for λ>0. For the first case, the interaction grows considerably as the spinon separation is increased and leads to confinement. On the other hand, the case λ>0 may lead to deconfinement of spinons.