Theory of arbitrarily polarized quantum Hall states: Filling fractions and wave functions

We propose a global model which accounts for almost all the observed quantum Hall states in terms of an Abelian doublet of Chern-Simons gauge fields, with the strength of the Chern-Simons term given by a coupling matrix. The model is employed within the composite fermion picture. We then determine the many body wave functions for arbitrarily polarized quantum Hall states by employing the doublet model which describes arbitrarily polarized quantum Hall states. Our findings recover the well known fully polarized Laughlin wave functions and unpolarized Halperin wave function for the filling fraction {ν}=2/5. We have also confirmed by an explicit one-loop computation that the Hall conductivity does indeed get quantized at those filling fractions that follow from the model. Finally, we have given a physical picture for the non-analytic nature of the wave functions, and shown that quantum fluctuations restore the Kohn mode. {} 1996 The American Physical Society.