Fractional Quantum Hall Effect from Phenomenological Bosonization

TL;DR

This paper introduces a phenomenological bosonization approach to model the fractional quantum Hall effect, capturing key features like bulk gapping, chiral edges, and fractional charges, aligning with experimental and theoretical insights.

Contribution

It presents a novel bosonization framework that effectively describes the fractional quantum Hall effect within a one-dimensional formalism, connecting to established theories.

Findings

Bulk becomes gapped at specific filling factors.

Edges are gapless, chiral, and carry fractional charge.

Results align with experimental observations and Laughlin wave function.

Abstract

In this paper we propose a model of the fractional quantum Hall effect within conventional one-dimensional bosonization. It is shown that in this formalism the resulting bosonized fermion operator corresponding to momenta of Landau gauge wave function is effectively two-dimensional. At special filling factors the bulk gets gapped, and the theory is described by a sine-Gordon model. The edges are shown to be gapless, chiral, and carrying a fractional charge. The hierarchy of obtained fractional charges is consistent with existing experiments and theories. It is also possible to draw a connection to composite fermion description and to the Laughlin many-body wave function.