SU(4) quantum coherence and interlayer tunneling in bilayer quantum Hall systems

We construct an effective Hamiltonian for bilayer quantum Hall ferromagnets, where the SU(4) nonlinear sigma model supports the SU(4) quantum coherence. At ν=1 there are three independent soft waves and three basic skyrmions. At ν=2 there exist two phases in each of which there are one soft wave and one biskyrmion. Interlayer tunneling occurs via the pseudospin soft mode not only at ν=1 but also at ν=2.