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.

arXiv comment6+8 pages. Accepted version to Physical Review Research Letters!

References in corpus (31)

• Noncommutative Field Theory
• Rapidly Rotating Atomic Gases
• Fractons
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Fracton Phases of Matter
• Bose-Einstein Condensates with Large Number of Vortices
• Fracton-Elasticity Duality
• Fracton hydrodynamics
• Quantum Hall states as matrix Chern-Simons theory
• Observation of Tkachenko Oscillations in Rapidly Rotating Bose-Einstein Condensates
• Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
• Towards classification of Fracton phases: the multipole algebra
• Quantum Melting and Absence of Bose-Einstein Condensation in Two-Dimensional Vortex Matter
• Redundancies in Nambu-Goldstone Bosons
• Tkachenko modes of vortex lattices in rapidly rotating Bose-Einstein condensates
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Quantum Hall Physics = Noncommutative Field Theory
• The dipolar Bose-Hubbard model
• Vortex lattices in rapidly rotating Bose-Einstein condensates: modes and correlation functions
• Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting
• Ground State and Tkachenko Modes of a Rapidly Rotating Bose-Einstein Condensate in the Lowest Landau Level State
• Hohenberg-Mermin-Wagner-type theorems and dipole symmetry
• Non-commutative Chern-Simons for the Quantum Hall System and Duality
• Non-commutative field theory and composite Fermi Liquids in some quantum Hall systems
• Effective field theory of a vortex lattice in a bosonic superfluid
• Higher-Rank Tensor Non-Abelian Field Theory: Higher-Moment or Subdimensional Polynomial Global Symmetry, Algebraic Variety, Noether's Theorem, and Gauging
• Tkachenko waves
• Lifshitz gauge duality
• Bosonic superfluid on lowest Landau level
• Exact Tkachenko modes and their damping in the vortex lattice regime of rapidly rotating bosons
• Uncertainty Principle and Off-Diagonal Long Range Order in the Fractional Quantum Hall Effect

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