Grassmannian Fields and Doubly Enhanced Skyrmions in Bilayer Quantum Hall system at $\nu=2$

At the filling factor $\nu=2$ the bilayer quantum Hall system has three phases, the ferromagnetic phase (spin phase), the spin singlet phase (ppin phase) and the canted antiferromagnetic phase. We analyze soft waves and quasiparticle excitations in the spin and ppin phases. It is shown that the dynamic field is the Grassmannian G$_{4,2}$ field carrying four complex degrees of freedom. In each phase there are four complex soft waves (pseudo-Goldstone modes) and one kind of skyrmion excitations (G$_{4,2}$ skyrmions) flipping either spins or pseudospins coherently. An intriguing property is that a quasiparticle is a G$_{4,2}$ skyrmion essentially consisting of two CP$^{3}$ skyrmions and thus possesses charge $2e$.