Effective field theory for the bulk and edge states of quantum Hall statesin unpolarized single layer and bilayer systems - art. no. 085306

We present an effective theory for bulk fractional quantum hall (FQH) state s in spin-polarized bilayer and spin-1/2 single-layer two-dimensional elect ron 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. W e find that the minimal effective theory contains two propagating edge mode s that carry charge and energy, and two nonpropagating topological modes re sponsible for the statistics of the excitations. We give a detailed descrip tion of the effective theory for spin-singlet states, symmetric bilayer sta tes, and for the (m,m,m) states. We explicitly calculate. for a number of c ases of interest, the operators that create the elementary excitations, the ir bound states, and the electron. We also discuss the scaling behavior of the tunneling conductances in different situations: internal tunneling, tun neling between identical edges, and tunneling into a FQH state from a Fermi liquid.