Effective field theory for the superfluid vortex lattice from coset construction

TL;DR

This paper develops an effective field theory for vortex lattices in rotating Bose-Einstein condensates, using symmetry principles and coset construction to describe the Tkachenko mode and its interactions.

Contribution

It introduces a novel effective field theory framework based on symmetry and coset methods for vortex lattices in trapped condensates, including higher-order interactions.

Findings

The theory correctly reproduces the gapless Tkachenko mode.

It satisfies Kohn's theorem within the constructed framework.

The next-to-leading order action includes cubic interaction terms.

Abstract

Guided by symmetry principles, we construct an effective field theory that captures the long-wavelength dynamics of two-dimensional vortex crystals observed in rotating Bose-Einstein condensates trapped in a harmonic potential. By embedding the system into Newton--Cartan spacetime and analyzing its isometries, we identify the appropriate spacetime symmetry group for trapped condensates at finite angular momentum. After introducing a coarse-grained description of the vortex lattice we consider a homogeneous equilibrium configuration and discuss the associated symmetry breaking pattern. We apply the coset construction method to identify covariant structures that enter the effective action and discuss the physical interpretation of the inverse Higgs constraints. We verify that Kohn's theorem is satisfied within our construction and subsequently focus on the gapless sector of the theory. In this regime, the effective theory accommodates a single gapless excitation--the Tkachenko mode--for which we construct both the leading-order and next-to-leading-order actions, the latter including cubic interaction terms.