Soliton and Domain Wall in the Self-Dual CP(1) Model

TL;DR

This paper studies soliton and domain wall solutions in a reduced 1+1 dimensional self-dual CP(1) model coupled to a Chern-Simons gauge field, revealing detailed equations and numerical solutions.

Contribution

It introduces a dimensional reduction of the nonrelativistic CP(1) model with Chern-Simons coupling and analyzes soliton and domain wall solutions in the resulting inhomogeneous Landau-Lifshitz system.

Findings

Hamiltonian is Bogomol'nyi bounded from below

Derived detailed Bogomol'nyi equations

Numerical solutions of the equations are presented

Abstract

We perform the dimensional reduction of the nonrelativistic CP(1) model coupled to an Abelian Chern-Simons gauge field in the self-dual limit, and investigate the soliton and domain wall solutions of the emerging 1+1 dimensional self-dual spin system. This system is described by inhomogeneous Landau-Lifshitz system with an extra non-local term. The Hamiltonian is Bogomol'nyi bounded from below and has four adjusting parameters. The Bogomol'nyi equation is described in detail in analogy with the Newtonian equation of motion and its numerical solution is presented.