Nonrelativistic Chern-Simons vortices from the constrained Hamiltonian formalism

Summary

Abstract

The Jackiw-Pi model of the self-gravitating gas of nonrelativistic bosons coupled to the Chern-Simons gauge field is known to exhibit asymptotically vanishing, lump-like soliton solutions. Here we discuss a recently proposed generalisation of this theory, which is applicable to systems of repulsive particles and allows to incorporate asymptotically nonvanishing fields, in particular topological vortices. We demonstrate the absence of the condensate state in the Jackiw-Pi model, relate this fact to a particular Lagrangian formulation of its nongauged precursor and derive the new model by modifying this Lagrangian appropriately and using it as a basis for the gauge theory. Reformulating the modified model as a constrained Hamiltonian system allows us to find the self-duality limit in the pure Chern-Simons and in the mixed Chern-Simons-Maxwell cases. These self-duality equations are shown to exhibit both asymptotically nonvanishing topological vortices and lump solitons.

Introduction

Vortices, topologically nontrivial localized structures, lie at the heart of all theories of particles with fractional statistics. It is these collective excitations of the field quanta that are considered as candidates for anyonic objects in the quasi-planar condensed matter physics. More precisely, in the case of the charged matter interacting with the Maxwell field, the anyon is a bound state of an (electrically neutral) vortex and a field quantum, a “flux” and a “charge”. If the gauge field is of the Chern-Simons type, the vortex is no more electrically neutral and behaves as an anyon itself.