Effective field theory for the bulk and edge states of quantum Hall states in unpolarized single layer and bilayer systems

We present an effective theory for bulk fractional quantum hall (FQH) states in spin-polarized bilayer and spin-1/2 single-layer two-dimensional electron gases in high magnetic fields consistent with the requirement of global gauge invariance on systems with periodic boundary conditions. We derive a theory for the edge states that follows naturally from this bulk theory. We find that the minimal effective theory contains two propagating edge modes that carry charge and energy, and two nonpropagating topological modes responsible for the statistics of the excitations. We give a detailed description of the effective theory for spin-singlet states, symmetric bilayer states, and for the (m,m,m) states. We explicitly calculate. for a number of cases of interest, the operators that create the elementary excitations, their bound states, and the electron. We also discuss the scaling behavior of the tunneling conductances in different situations: internal tunneling, tunneling between identical edges, and tunneling into a FQH state from a Fermi liquid.