Effective-Field-Theory Model for the Fractional Quantum Hall Effect

Starting directly from the microscopic Hamiltonian, we derive a field-theory model for the fractional quantum Hall effect. By considering an approximate coarse-grained version of the same model, we construct a Landau-Ginzburg theory similar to that of Girvin. The partition function of the model exhibits cusps as a function of density and the Hall conductance is quantized at filling factors $\nu ={\mathrm{}(2k-1)\mathrm{}}^{-1\mathrm{}}$ with $k$ an arbitrary integer. At these fractions the ground state is incompressible, and the quasiparticles and quasiholes have fractional charge and obey fractional statistics. Finally, we show that the collective density fluctuations are massive.