Effective theories of the fractional quantum Hall effect at generic filling fractions

Abstract

We propose effective theories that describe the fractional quantum Hall effect (FQHE) states for the generic filling fractions \ensuremath{\nu}=1/ t${sum}_{\mathit{I}}$ (1/${\mathit{m}}_{\mathit{I}}$) where ${\mathit{m}}_{\mathit{I}}$ are integers. The theories describe the microscopic FQHE states proposed by Jain. We calculate charges and statistics of quasiparticles in these states. The structure of the edge states is derived directly from the underlying effective theory in the bulk. Our results are shown to be consistent with those obtained from the microscopic theory.