Nonperturbative approach to the quantum Hall bilayer

We develop a nonperturbative approach to the quantum Hall bilayer (QHB) at \nu=1 using trial wave functions. We predict phases of the QHB for arbitrary distance d and, our approach, in a dual picture, naturally introduces a new kind of quasiparticles - neutral fermions. Neutral fermion is a composite of two merons of the same vorticity and opposite charge. For small d (i.e. in the superfluid phase), neutral fermions appear as dipoles. At larger d dipoles dissociate into the phase of the two decoupled Fermi-liquid-like states. This scenario is relevant for the experimental situation where impurities lock charged merons. In a translation invariant (clean) system, continuous creation and annihilation of meron-antimeron pairs evolves the QHB toward a paired phase. The quantum fluctuations fix the form of the pairing function to g(z)=1/z^*. A part of the description of the paired phase is the 2D superconductor i.e. BF Chern-Simons theory. The paired phase is not very distinct from the superfluid phase.