Lowest Landau level bosonization

TL;DR

This paper introduces a bosonization approach for a two-dimensional electron gas at filling factor one, mapping fermionic excitations to bosons and analyzing their interactions and relation to skyrmions.

Contribution

It develops a bosonization scheme for the quantum Hall system at u=1, connecting magnetic excitons to bosons and exploring their interactions and topological excitations.

Findings

Bosonic dispersion matches RPA calculations.

Interaction term reveals two-boson bound states.

Semiclassical limit aligns with skyrmion models.

Abstract

We develop a bosonization scheme for the two-dimensional electron gas in the presence of an uniform magnetic field perpendicular to the two-dimensional system when the filling factor \nu = 1. We show that the elementary neutral excitations of this system, known as magnetic excitons, can be treated approximately as bosons and we apply the method to the interacting system. We show that the Hamiltonian of the fermionic system is mapped into an interacting bosonic Hamiltonian, where the dispersion relation of the bosons agrees with previous RPA calculations. The interaction term accounts for the formation of two-boson bound states. We discuss a possible relation between these excitations and the skyrmion-antiskyrmion pair, in analogy with the ferromagnetic Heisenberg model. Finally, we analyze the semiclassical limit of the interacting bosonic Hamiltonian and show that the results are in agreement with those derived from the model of Sondhi {\it et al.} for the quantum Hall skyrmion.