Phase transition and spin–wave dispersion in quantum Hall bilayers at filling factor ν=1

We present an effective Hamiltonian for a bilayer quantum Hall system at filling factor ν=1 neglecting charge fluctuations. Our model is formulated in terms of spin and pseudospin operators and is an exact representation of the system within the above approximation. We analyze its low-lying excitations in terms of spin–wave theory. Moreover we add to previous first-principle exact-diagonalization studies concentrating on the quantum phase transition seen in this system.