Microscopic formulation of the hierarchy of quantized Hall states

TL;DR

This paper introduces explicit wave functions for the hierarchy of fractional quantum Hall states, develops a method to evaluate their properties, and analyzes their relation to model Hamiltonians, providing insights into their physical characteristics.

Contribution

It proposes explicit wave functions for fractional quantum Hall hierarchy states and extends the adiabatic transport method to evaluate quasiparticle properties.

Findings

Wave functions show excellent overlap with exact ground states for small systems.

Quasiparticle charges and statistics are evaluated using the generalized adiabatic transport.

None of the proposed states are exact ground states of simple two-body Hamiltonians.

Abstract

Explicit wave functions for the hierarchy of fractionally quantized Hall states are proposed, and a method for integrating out the quasiparticle coordinates in the spherical geometry is developed. Their energies and overlaps with the exact ground states for small numbers of particles with Coulomb interactions are found to be excellent. We then generalize the adiabatic transport argument of Arovas, Schrieffer, and Wilczek to evaluate quasiparticle charges and statistics, and show that none of the proposed states is the exact ground state of any model Hamiltonian with two-body interactions only.