Noncommutative field theory of the Tkachenko mode: Symmetries and decay rate

Journal Article · 25 February 2024 · Physical Review Research

DOI: https://doi.org/10.1103/PhysRevResearch.6.L012040 · OSTI ID:2311911

Du, Yi-Hsien ; Moroz, Sergej; Nguyen, Dung Xuan ; Son, Dam Thanh

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 $\mathrm{\Gamma }$ of the Tkachenko mode scales with its energy $E$ as $\mathrm{\Gamma }\sim E^3$ in the low-energy limit. We also discuss the width of the Tkachenko mode at a small temperature. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0009924; SC0009924
• OSTI ID: 2311911
• Journal Information: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 1 Vol. 6; ISSN 2643-1564; ISSN PPRHAI
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English