Hopf term and the effective Lagrangian for the Skyrmions in a two-dimensional electron gas at small g-factor

TL;DR

This paper derives an effective Lagrangian for Skyrmions in a two-dimensional electron gas with small g-factor, revealing a non-zero Hopf term and detailed Skyrmion interactions, advancing understanding of quasiparticle dynamics in quantum Hall systems.

Contribution

It provides a transparent derivation of the effective Lagrangian including a rigorously determined Hopf term and detailed Skyrmion interactions up to fourth order in derivatives.

Findings

Non-zero Hopf term with a rigorously determined prefactor

Complete Skyrmion-Skyrmion interaction up to fourth order in derivatives

Enhanced understanding of quasiparticle dynamics in quantum Hall systems

Abstract

We study interacting electrons in two dimensions moving in the lowest Landau level under the condition that the Zeeman energy is much smaller than the Coulomb energy and the filling factor is one. In this case, Skyrmion quasiparticles play an important role. Here, we present a simple and transparent derivation of the corresponding effective Lagrangian. In its kinetic part, we find a non-zero Hopf term the prefactor of which we determine rigorously. In the Hamiltonian part, we calculate, by means of a gradient expansion, the Skyrmion-Skyrmion interaction completely up to fourth order in spatial derivatives.