Fermi-liquid shell model for N electrons on a spherical surface: A test of the composite fermion hierarchy picture

Abstract

The extension of the Jain theory of fractional quantum Hall states to all odd denominator filling states is proposed in analogy to the Haldane hierarchy. The composite fermion hierarchy is a natural consequence of the Fermi-liquid quasiparticle picture when applied to composite fermion excitations on the sphere. It is shown that the “finite size corrections” defined as 1/ ν−2 S/( N−1), where ν is the filling factor, 2 S the magnetic monopole strength in flux quanta, and N the number of electrons, exhibit periodicity as a function of 2 S with period 2( N−1). The results of numerical diagonalization for ν= 4 11 and ν= 4 13 ( N=8) show no indication of a condensed state. It is also the case for the system of 4QE of the 2 3 Jain state ( N=12) seen as the “half-filled state” of quasielectrons.