Chern–Simons structure of solitons in the model of the discrete (2+1)D nonlinear Schrödinger equation

The structure of solitons in the model of gauged nonlinear Schrödinger equation on (2+1)D lattice and their contribution to the value of the number of particles are considered. It is shown that in the region of small values of the Chern–Simons coefficient k, there exists a universal attraction between localized field configurations. The universal topological character of the Chern–Simons correlations is determined by the degree k of the braiding of the excitation world lines. The attraction due to the Chern–Simons correlations has been obtained under assumption of the discretization of the temporal variable. For k=2, this phenomenon may be a dynamic origin of the semion pairing in planar systems.