Anyon Field Theory and Fractional Quantum Hall States

Abstract

We analyze the fractional quantum Hall effect by using an anyon field theory defined perturbatively in terms of a boson field. It is shown explicitly that there exist fractional quantum Hall (FQH) states which are condensed phases of bosonized electrons at zero momentum. When the Coulomb interaction is switched off, these states are degenerate with other states which are obtained by solving a certain self-dual equation. Taking into account the electron spin degrees of freedom we also show the existence of spin-singlet FQH states at the half-filling (ν = 1/2) and find vortex soliton excitations carrying the electric charge e/4. Furthermore, by using singular gauge transformations, we construct field theories of vortex solitons and derive the hierarchy of hte FQH states.