Ring-shaped fractional quantum Hall liquids with hard-wall potentials

TL;DR

This paper investigates ring-shaped bosonic fractional quantum Hall liquids with hard-wall confinement, proposing new trial wave functions, analyzing their spectra, and exploring edge and quasihole excitations for potential experimental applications.

Contribution

It introduces extended Jack polynomial-based trial wave functions for ring-shaped FQH states and analyzes their spectral properties under various confinement potentials.

Findings

High overlap of trial wave functions with exact eigenstates across potentials

Identification of a degenerate ground state manifold with a single potential

Organization of edge excitations and quasiholes in the ring geometry

Abstract

We study the physics of $\nu=1/2$ bosonic fractional quantum Hall droplets confined in a ring-shaped region delimited by two concentric cylindrically symmetric hard-wall potentials. Trial wave functions based on an extension of the Jack polynomial formalism including two different chiral edges are proposed and validated for a wide range of confinement potentials in terms of their excellent overlap with the eigenstates numerically found by exact diagonalization. In the presence of a single repulsive potential centered in the origin, a recursive structure in the many-body spectra and a massively degenerate ground state manifold are found. The addition of a second hard-wall potential confining the fractional quantum Hall droplet from the outside leads to a non-degenerate ground state containing a well defined number of quasiholes at the center and, for suitable potential parameters, to a clear organization of the excitations on the two edges. The utility of this ring-shaped configuration in view of theoretical and experimental studies of subtle aspects of fractional quantum Hall physics is outlined.