Electrons in a Strong Magnetic Field on a Disk

TL;DR

This paper investigates the properties of electrons in a strong magnetic field on a finite disk, analyzing exact diagonalizations and the validity of quasiparticle concepts, especially at filling factor 1/3, and compares results with trial wave functions.

Contribution

It provides the first detailed comparison of exact diagonalization results with hierarchical quasiparticle theories for electrons in a magnetic field on a disk.

Findings

The 1/3 state is identifiable with short-range interactions but not with Coulomb interactions.

Quasihole theory aligns well with the spectra, but quasielectron analysis is complicated by finite size effects.

Extrapolated quasielectron energies from exact results closely match the best trial wave functions.

Abstract

The problem of interacting electrons moving under the influence of a strong magnetic field in two dimensions on a finite disk is reconsidered. First, the results of exact diagonalizations for up to $N=9$ electrons for Coulomb as well as for a short--range interaction are used in the search for a peculiar ground state corresponding to filling factor $1/3$. Not for the Coulomb, but only for the short--range interaction, can the $1/3$--state be safely identified amongst the spectra of various filling factors close to $1/3$. Second, the propositions of the concept of quasiparticles, as used in the hierarchical theory, are examined in view of the exact results for the disk geometry. Whereas the theory for the quasiholes is in complete accordance with the spectra, for the quasielectrons, finite size corrections make an analysis difficult. For the quasielectron energy, an extrapolation to $N \rightarrow \infty$ is given and compared with the corresponding extrapolations of three different proposals for trial wave functions. While the limiting value for the best trial wave function is very close to the limit of the exact results, the behavior of the finite size corrections of the exact energies and of the trial wave functions, respectively, is qualitatively rather different.