I. WEN-TYPE TOPOLOGICAL PHASES: THE FRACTIONAL QUANTUM HALL EFFECT A. Chern-Simons theory I: flux attachment and statistics change

where m = 0, 1, . . . labels angular momentum. For m = 1 the Laughlin state is just a Slater determinant for the filled lowest Landau level, but for higher m it is believed not to be a sum of any finite number of Slater determinants in the N →∞ limit. We explained the origin of this wavefunction using the pseudopotential approach introduced by Haldane: it is the maximum-density zero-energy state of a repulsive interaction that vanishes for relative angular momentum greater than or equal to m. We checked that its density is ν = 1/m by looking at the degree of the polynomial factor, which is directly related to 〈r〉, and argued that it contains “quasihole” excitations of charge −q/m, where q is the charge of the electrons. The wavefunction for a quasihole at z0 is