Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level

TL;DR

This paper develops a new basis for composite fermions within the lowest Landau level, enabling large-scale Monte Carlo simulations that provide precise energies and insights into fractional quantum Hall states and exciton formation.

Contribution

It introduces a basis for composite fermions in the lowest Landau level, allowing accurate large-system simulations and deeper understanding of FQHE states without higher Landau level assumptions.

Findings

Ground state energies estimated with ~0.1% accuracy

Gaps computed at a few percent precision

FQHE unstable to exciton creation at fillings ≤ 1/9

Abstract

Single particle basis functions for composite fermions are obtained from which many-composite fermion states confined to the lowest electronic Landau level can be constructed in the standard manner, i.e., by building Slater determinants. This representation enables a Monte Carlo study of systems containing a large number of composite fermions, yielding new quantitative and qualitative information. The ground state energy and the gaps to charged and neutral excitations are computed for a number of fractional quantum Hall effect (FQHE) states, earlier off-limits to a quantitative investigation. The ground state energies are estimated to be accurate to \sim 0.1% and the gaps at the level of a few percent. It is also shown that at Landau level fillings smaller than or equal to 1/9 the FQHE is unstable to a spontaneous creation of excitons of composite fermions. In addition, this approach provides new conceptual insight into the structure of the composite fermion wave functions, resolving in the affirmative the question of whether it is possible to motivate the composite fermion theory entirely within the lowest Landau level, without appealing to higher Landau levels.