Toward a new theory of the fractional quantum Hall effect: The many-body spectra and energy gaps at $\nu<1$

TL;DR

This paper investigates the many-body spectra and energy gaps of small two-dimensional electron systems in the fractional quantum Hall regime, challenging existing wave function models and elucidating the nature of ground and excited states.

Contribution

It provides a detailed analysis of the energy spectra and physical properties of small electron systems at various filling factors, offering new insights into the true ground states beyond Laughlin's wave function.

Findings

Energy gaps are explained by specific physical mechanisms.

The true ground state differs significantly from Laughlin's variational wave function.

Electron densities and spectra vary continuously with magnetic field.

Abstract

In a recent paper (arXiv:2206.05152v4), using the exact diagonalization technique, I calculated the energy and other physical properties (electron density, pair correlation function) of a system of $N\le 7$ two-dimensional electrons at the Landau level filling factor $\nu=1/3$, and showed that the variational many-body wave function proposed for this filling factor by Laughlin is far from the true ground state. In this paper I continue to study exact properties of a small ($N\le 7$) system of two-dimensional electrons lying on the lowest Landau level. I analyze the energies and electron densities of the systems with $N\le 7$ electrons continuously as a function of the magnetic field in the range $1/4\lesssim\nu<1$. The physical mechanisms of the appearance of energy gaps in many-particle electron spectra are elucidated. The results obtained clarify the true nature of the ground and excited states of the considered systems.