Solitons and Quasielectrons in the Quantum Hall Matrix Model

TL;DR

This paper introduces a finite quantum Hall matrix model that successfully incorporates fractionally charged quasielectrons as BPS solitons and quasiholes, providing a new theoretical framework for understanding quantum Hall states.

Contribution

It presents a novel finite matrix model incorporating quasielectrons as BPS solitons in a noncommutative field theory, advancing the theoretical understanding of quantum Hall effects.

Findings

Quasielectrons are modeled as BPS solitons and quasiholes.

Density profiles for droplets, quasiholes, and quasielectrons are calculated.

The charge density in the matrix model is properly defined.

Abstract

We show how to incorporate fractionally charged quasielectrons in the finite quantum Hall matrix model.The quasielectrons emerge as combinations of BPS solitons and quasiholes in a finite matrix version of the noncommutative $\phi^4$ theory coupled to a noncommutative Chern-Simons gauge field. We also discuss how to properly define the charge density in the classical matrix model, and calculate density profiles for droplets, quasiholes and quasielectrons.