Quasiparticle Aggregation in the Fractional Quantum Hall Effect

Abstract

Quasiparticles in the Fractional Quantum Hall Effect behave qualitatively like electrons confined to the lowest landau level, and can do everything electrons can do, including condense into “second generation” Fractional Quantum Hall ground states. I review in this paper the reasoning leading to variational wavefunctions for ground state and quasiparticles in the 1/3 effect. I then show how two-quasiparticle eigenstates are uniquely determined from symmetry, and how this leads in a natural way to variational wavefunctions for composite states which have the correct densities (2/5, 2/7, ...). I show in the process that the boson, anyon and fermion representations for the quasiparticles used by Haldane, Halperin and me are all equivalent. I demonstrate a simple way to derive Halperin’s multiple-valued quasiparticle wavefunction from the correct single-valued electron wavefunction.