Trial Wavefunctions for the Goldstone Mode in ?=1/2+1/2 Quantum Hall Bilayers

Based on the known physics of the excitonic superfluid or 111 state of the quantum Hall $\nu=1/2+1/2$ bilayer, we create a simple trial wavefunction ansatz for constructing a low energy branch of (Goldstone) excitations by taking the overall ground state and boosting one layer with respect to the other. This ansatz works extremely well for any interlayer spacing. For small $d$ this is simply the physics of the Goldstone mode, whereas for large $d$ this is a reflection of composite fermion physics. We find hints that certain aspects of composite fermion physics persist to low $d$ whereas certain aspects of Goldstone mode physics persist to high $d$. Using these results we show nonmonotonic behavior of the Goldstone mode velocity as a function of $d$.