Integer quantum Hall effect for hard-core bosons and a failure of bosonic Chern-Simons mean-field theories for electrons at half-filled Landau level

TL;DR

This paper demonstrates that the integer quantum Hall effect occurs in a system of hard-core bosons at half-filling, revealing limitations of bosonic Chern-Simons mean-field theories for electrons in Landau levels.

Contribution

It shows that the mean-field approximation fails for mapping electrons at half-filling to bosonic systems due to the emergence of the integer quantum Hall effect in the bosonic model.

Findings

Hard-core bosons at unit filling exhibit an integer quantum Hall effect.

Mean-field approximation fails for half-filled Landau level mapping.

Bosonic Chern-Simons theories do not accurately describe electrons at half-filling.

Abstract

Field-theoretical methods have been shown to be useful in constructing simple effective theories for two-dimensional (2D) systems. These effective theories are usually studied by perturbing around a mean-field approximation, so the question whether such an approximation is meaningful arises immediately. We here study 2D interacting electrons in a half-filled Landau level mapped onto interacting hard-core bosons in a magnetic field. We argue that an interacting hard-core boson system in a uniform external field such that there is one flux quantum per particle (unit filling) exhibits an integer quantum Hall effect. As a consequence, the mean-field approximation for mapping electrons at half-filling to a boson system at integer filling fails.