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Advances in Condensed Matter Physics
Volume 2011, Article ID 815169, 7 pages
Research Article

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

1TCM Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, UK
2Rudolf Peierls Centre for Theoretical Physics, Oxford University, Oxford OX1 3NP, UK

Received 12 September 2010; Accepted 28 October 2010

Academic Editor: Yogesh Joglekar

Copyright © 2011 Gunnar Möller and Steven H. Simon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Based on the known physics of the excitonic superfluid or 111 state of the quantum Hall 𝜈 = 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 .