  The Coulomb exchange 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 3
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 3 independent skyrmion states apart from the
translational degree of freedom. They are CP$^{3}$ skyrmions enjoying the
spin-charge entanglement confined within the \LLL.
