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

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 $\nu =1\mathrm{/}3$, 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 $1\mathrm{/}4\lesssim \nu <1$. 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.