Luttinger States at the Edge

Abstract

An effective wavefunction for the edge excitations in the Fractional quantum Hall effect can be found by dimensionally reducing the bulk wavefunction. Treated this way the Laughlin $ν=1/(2n+1)$ wavefunction yields a Luttinger model ground state. We identify the edge-electron field with a Luttinger hyper-fermion operator, and the edge electron itself with a non-backscattering Bogoliubov quasi-particle. The edge-electron propagator may be calculated directly from the effective wavefunction using the properties of a one-dimensional one-component plasma, provided a prescription is adopted which is sensitive to the extra flux attached to the electrons.