Interlayer exchange interactions, SU(4) soft waves, and skyrmions in bilayer quantum Hall ferromagnets

The exchange Coulomb interaction is the driving force for quantum coherence in quantum Hall systems. We construct a microscopic Landau-site Hamiltonian for the exchange interaction in bilayer quantum Hall ferromagnets, which is characterized by the SU(4) isospin structure. By taking a continuous limit, the Hamiltonian gives rise to the SU(4) nonlinear sigma model in the von Neumann-lattice formulation. The ground-state energy is evaluated at filling factors nu = 1,2,3,4. It is shown at nu = 1 that there are three independent soft waves, where only one soft wave is responsible for the coherent tunneling of electrons between the two layers. It is also shown at nu = 1 that there are three independent skyrmion states apart from the translational degree of freedom. They are CP3 skyrmions enjoying the spin-charge entanglement confined within the lowest Landau level.