Meron deconfinement in the quantum Hall bilayer at intermediate distances

Quantum Hall bilayer phase diagram with respect to interlayer distance bears a remarkable similarity with phase diagrams of strongly correlated systems as a function of doping, with magnetic ordering on the one end and Fermi-liquid-like behavior on the other. Moreover, it has been suggested [Phys. Rev. Lett. 101, 176803 (2008)] that a BCS correlated state of composite fermions with $p$-wave pairing may exist in the intermediate region. In the same region, an exact diagonalization study in the torus geometry [Phys. Rev. B 69, 045319 (2004)] pointed out the existence of state(s) with pseudospin spiraling order. Here we reconcile these two descriptions of the intermediate state by considering the underlying bosonic representation of the composite fermion paired state in the long-distance limit, and by performing extensive exact diagonalizations on the torus. We argue that the spiraling states belong to the manifold of degenerate ground state(s), and are a consequence of Bose condensation of the quasiparticles (with critical algebraic correlations) at nonzero momenta in the two pseudospin states. The spiraling states, generated in this way as spin textures, can be identified with meron-antimeron constructions. Thus, merons---the fractionally charged vortex excitations of the $\mathit{XY}$ magnetically ordered state---constitute some of the topological sectors. It follows that merons are deconfined in the intermediate state, and allow for a smooth transition between the magnetically ordered and Fermi-liquid-like phases, in which they are bound in pairs.