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

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.

6+8 pages. Accepted version to Physical Review Research Letters!

References in corpus (5)

• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• The dipolar Bose-Hubbard model
• Hohenberg-Mermin-Wagner-type theorems and dipole symmetry
• Lifshitz gauge duality
• Bosonic superfluid on lowest Landau level

Cited by in corpus (7)

• Quantum vortex lattice: Lifshitz duality, topological defects and multipole symmetries
• On quantum melting of superfluid vortex crystals: from Lifshitz scalar to dual gravity
• Topological Dipole Insulator
• Non-commutative effective field theory of the lowest Landau level superfluid
• Semiclassical states localized on a one-dimensional manifold and governed by the nonlocal NLSE with an anti-Hermitian term
• Effective field theory for the superfluid vortex lattice from coset construction
• Quadrupole-conserving dynamics in the non-commutative plane