An exact spin mapping is identified to simplify the recently proposed hard-core boson description [Demler and Das Sarma, Phys. Rev. Lett. $82,$ 3895 (1999)] of the bilayer quantum Hall system at filling factor 2. The effective spin model describes an easy-plane ferromagnet subject to an external Zeeman field. The phase diagram of this effective model is determined exactly, while the Goldstone-mode spectrum, order parameter stiffness and Kosterlitz-Thouless temperature in the canted antiferromagnetic phase are computed approximately.

• Received 12 May 1999

DOI:https://doi.org/10.1103/PhysRevB.60.15578