Quasi-hole solutions in finite noncommutative Maxwell-Chern-Simons theory

TL;DR

This paper explores finite noncommutative Maxwell-Chern-Simons theory, revealing a spectrum of solitons and quasi-holes with quantized flux and charge, extending the understanding of quantum Hall effect models.

Contribution

It introduces a finite matrix model with boundary fluctuations for Maxwell-Chern-Simons theory, uncovering new soliton and quasi-hole solutions with quantized properties.

Findings

Existence of solitons with nontrivial magnetic flux

Discovery of quasi-holes with quantized charge

Identification of a spectral gap for quasi-hole charges

Abstract

We study Maxwell-Chern-Simons theory in 2 noncommutative spatial dimensions and 1 temporal dimension. We consider a finite matrix model obtained by adding a linear boundary field which takes into account boundary fluctuations. The pure Chern-Simons has been previously shown to be equivalent to the Laughlin description of the quantum Hall effect. With the addition of the Maxwell term, we find that there exists a rich spectrum of excitations including solitons with nontrivial "magnetic flux" and quasi-holes with nontrivial "charges", which we describe in this article. The magnetic flux corresponds to vorticity in the fluid fluctuations while the charges correspond to sources of fluid fluctuations. We find that the quasi-hole solutions exhibit a gap in the spectrum of allowed charge.