Vortex description of quantum Hall ferromagnets

TL;DR

This paper links vortex theory to quantum Hall ferromagnets, showing that elementary excitations are composite particles and that pure electron states are absent in the strong coupling regime.

Contribution

It establishes a novel correspondence between vortex moduli space and the phase space of Chern-Simons matrix theory for quantum Hall ferromagnets.

Findings

Elementary excitations are identified as vortex states.

Pure electron states are absent in the strong coupling region.

Composite particle states dominate in the strong coupling regime.

Abstract

We study particle states of quantum Hall ferromagnet from the viewpoint of the incompressible fluid description. It is shown that phase space of Chern-Simons matrix theory which is an effective theory for the incompressible fluid is equivalent to moduli space of vortex theory. According to this correspondence, elementary excitations in vortex theory are identified as particle states in quantum Hall ferromagnet, and thus we propose that a pure electron state is absent from the strong coupling region but only a composite particle state is present.