Effective field theory of a vortex lattice in a bosonic superfluid

TL;DR

This paper develops a low-energy effective theory for a vortex lattice in a two-dimensional bosonic superfluid, revealing unique excitation modes and Hall responses influenced by external rotation and symmetry considerations.

Contribution

It introduces a novel effective field theory for vortex lattices in bosonic superfluids using boson-vortex duality, analyzing excitation spectra and Hall responses.

Findings

Identifies gapped Kohn and elliptically polarized Tkachenko modes.

Shows external rotation induces Hall responses and breaks symmetries.

Suggests zero-frequency Hall viscosity vanishes in the vortex lattice.

Abstract

Using boson-vortex duality, we formulate a low-energy effective theory of a two-dimensional vortex lattice in a bosonic Galilean-invariant compressible superfluid. The excitation spectrum contains a gapped Kohn mode and an elliptically polarized Tkachenko mode that has quadratic dispersion relation at low momenta. External rotation breaks parity and time-reversal symmetries and gives rise to Hall responses. We extract the particle number current and stress tensor linear responses and investigate the relations between them that follow from Galilean symmetry. We argue that elementary particles and vortices do not couple to the spin connection which suggests that the Hall viscosity at zero frequency and momentum vanishes in a vortex lattice.