Non-commutative effective field theory of the lowest Landau level superfluid
Nandagopal Manoj (Caltech)
A 2+1d superfluid in a rapidly rotating trap forms an array of vortices, with collective “phonon” oscillations called Tkachenko modes. Ref. [1] argued based on the symmetries of the problem that an effective field theory describing these Tkachenko modes will be a field theory living on non-commutative space. In this talk, I present some ongoing work which elucidates the microscopic origin of these non-commutative fields, and a novel derivation of the effective field theory (EFT) for this superfluid using a coherent state path integral approach. Besides conceptual clarity, this approach also helps make quantitative predictions about the long-wavelength, low-energy behavior of the weakly interacting lowest Landau level superfluid — relevant to trapped BEC experiments.
[1] Y.-H. Du, S. Moroz, D. X. Nguyen, and D. T. Son, Phys. Rev. Res. 6, L012040 (2024).
[2] N. Manoj, arXiv:2502.03528