Noncommutative effective field theory of the lowest Landau level superfluid
Abstract
A (2+1)-dimensional superfluid in a rapidly rotating trap forms an array of vortices, with collective excitations called Tkachenko modes. Du et al. [Noncommutative field theory of the Tkachenko mode: Symmetries and decay rate Phys. Rev. Res. 6, L012040 (2024)] argued from an effective field theory viewpoint that these excitations are described by a field theory living on a noncommutative space. We elucidate the microscopic origin of these noncommutative fields, and present a derivation of the effective field theory for this superfluid using a lowest Landau level projected coherent state path-integral approach. Aside from conceptual clarity, this approach makes quantitative predictions about the long-wavelength, low-energy behavior in terms of the microscopic parameters of the short-range interacting lowest Landau level superfluid, relevant to trapped Bose-Einstein condensate experiments.
Copyright and License
©2025 American Physical Society
Acknowledgement
We thank J. Alicea, H. Goldman, X. Huang, D. X. Nguyen, V. Peri, L. Radzihovsky, and T. Senthil for useful discussions and valuable comments. We also thank the organizers of the Prospects in theoretical physics (PiTP) 2024 program at IAS, Princeton, for their hospitality where part of this work was done. This work was primarily led and supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center. We appreciate the support received from the Institute of Quantum Information and Matter.
Data Availability
The data that support the findings of this article are not publicly available. The data are available from the authors upon reasonable request.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2502.03528 (arXiv)
Funding
- United States Department of Energy
Dates
- Accepted
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2025-07-25