A Non-linear Sigma-model for Partially Polarized QH-states

TL;DR

This paper develops a covariant non-linear sigma model with Chern-Simons coupling to describe partially polarized quantum Hall states, capturing quasiparticle excitations with correct quantum numbers and energy properties.

Contribution

It introduces a new sigma model framework derived from Landau-Ginzburg theory to describe partially polarized quantum Hall states and their topological excitations.

Findings

Quasiparticles are represented as topological excitations with correct quantum numbers.

The model describes finite energy skyrmion-like excitations in quantum Hall systems.

Fully polarized states have spin determined by Coulomb and Zeeman interactions.

Abstract

We consider a two-component quantum Hall system within a Landau-Ginzburg theory with two Chern-Simons gauge fields. From this theory we derive a sigma model covariantly coupled to one Chern-Simons field and find mean field solutions that could describe partially polarized quantum Hall states. The quasiparticles in the original model, which have quantized charge and spin, are described in the covariant sigma model by topological excitations, with the correct quantum numbers. They have finite energy due to the presence of the Chern-Simons field, and closely resemble the skyrmions in the usual non-linear sigma model. For the fully polarized states the spin is no longer quantized, but determined by Coulomb and Zeeman interactions.