Non-Linear hydrodynamics and Fractionally Quantized Solitons at Fractional Quantum Hall Edge

TL;DR

This paper proposes that the non-linear dynamics of fractional quantum Hall edge states involve fractionally quantized solitons, governed by the quantum Benjamin-Ono equation, providing a potential signature of fractional charges.

Contribution

It introduces a non-linear model for FQH edge states using the quantum Benjamin-Ono equation, linking soliton behavior to fractional charge detection.

Findings

Fractionally quantized solitons can propagate along FQH edges.

Non-linear edge dynamics are governed by the quantum Benjamin-Ono equation.

Edge mode dispersion relates to the boundary layer of FQH states.

Abstract

We argue that dynamics of gapless Fractional Quantum Hall Edge states is essentially non-linear and that it features fractionally quantized solitons propagating along the edge. Observation of solitons would be a direct evidence of fractional charges. We show that the non-linear dynamics of the Laughlin's FQH state is governed by the quantum Benjamin-Ono equation. Non-linear dynamics of gapless edge states is determined by gapped modes in the bulk of FQH liquid. The dispersion of edge modes is traced to the double boundary layer of FQH states.