Chiral solitons from dimensional reduction of Chern-Simons gauged non-linear Schr\"odinger model of FQHE: classical and quantum aspects

TL;DR

This paper explores chiral solitons in a gauge theory model of the Fractional Quantum Hall Effect, deriving a new non-linear Schrödinger equation and analyzing classical and quantum properties of these solitons.

Contribution

It introduces a novel non-linear derivative Schrödinger equation for FQHE chiral excitations and investigates both classical and quantum aspects of the resulting solitons.

Findings

Discovery of a new non-linear Schrödinger equation for FQHE

Classical analysis of dark solitons with boundary conditions

Quantum analysis using semiclassical and RG methods

Abstract

The soliton structure of a gauge theory recently proposed to describe chiral excitations in the Fractional Quantum Hall Effect is investigated. A new type of non-linear derivative Schr\"odinger equation emerges as an effective description of the system that supports novel chiral solitons. We discuss the classical properties of solutions with vanishing and non-vanishing boundary conditions (dark solitons) and we explain their relation to integrable systems. The quantum analysis is also addressed in the framework of a semiclassical approximation improved by Renormalization Group arguments.