Trial wavefunctions for the Goldstone mode in \nu=1/2+1/2 quantum Hall bilayers

TL;DR

This paper introduces a simple trial wavefunction ansatz for the Goldstone mode in quantum Hall bilayers at 22 filling, capturing physics across different interlayer spacings and revealing nonmonotonic mode velocity behavior.

Contribution

It proposes a new trial wavefunction ansatz for Goldstone excitations that works across all interlayer spacings, bridging excitonic superfluid and composite fermion physics.

Findings

Ansatz accurately models Goldstone mode for all d

Hints of composite fermion physics at small d

Nonmonotonic Goldstone mode velocity as d varies

Abstract

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.