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Noncommutative Field Theory of the Tkachenko Mode: Symmetries and Decay Rate

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arxiv 2212.08671 v2 pith:MXZAPC4V submitted 2022-12-16 cond-mat.str-el cond-mat.quant-gashep-th

Yi-Hsien Du , Sergej Moroz , Dung Xuan Nguyen , Dam Thanh Son This is my paper · ORCID
classification cond-mat.str-elcond-mat.quant-gashep-th
keywords theoryfieldmodetkachenkononcommutativedecayeffectivegamma
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abstract

We construct an effective field theory describing the collective Tkachenko oscillation mode of a vortex lattice in a two-dimensional rotating Bose-Einstein condensate in the long-wavelength regime. The theory has the form of a noncommutative field theory of a Nambu-Goldstone boson, which exhibits a noncommutative version of dipole symmetry. From the effective field theory, we show that, at zero temperature, the decay width $\Gamma$ of the Tkachenko mode scales with its energy $E$ as $\Gamma\sim E^3$ in the low-energy limit. We also discuss the width of the Tkachenko mode at a small temperature.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 13 citations worldwide. Full citation record

  1. Breakdown of hydrodynamics in a Galilean quantum Hall crystal

    cond-mat.mes-hall 2024-12 conditional novelty 6.0 of 10

    In a Galilean-invariant quantum Hall crystal, nonlinear fluctuations destabilize the linear-response magnetophonon and drive its dynamical exponent from z=4 to z≈3.

  2. Effective Field Theories for Material Media

    hep-th 2026-07 accept novelty 4.0 of 10

    Spacetime-symmetry-breaking Goldstone EFTs systematically describe bulk and localized excitations of solids, fluids, and superfluids, with new thermodynamic identifications and corrected scattering rates.

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