# Bosonic superfluid on lowest Landau level

## TL;DR

This paper develops an effective field theory for a 2D bosonic superfluid on the lowest Landau level, revealing a Berry term that influences collective excitations and Hall responses without inducing Hall viscosity.

## Contribution

It introduces a novel Berry term in the effective field theory that affects superfluid dynamics and Hall responses in the lowest Landau level setting.

## Key findings

- Berry term modifies Tkachenko oscillation spectrum
- Hall conductivity acquires quadratic momentum dependence
- No non-dissipative Hall viscosity is generated

## Abstract

We develop a low-energy effective field theory of a two-dimensional bosonic superfluid on the lowest Landau level at zero temperature and identify a Berry term that governs the dynamics of coarse-grained superfluid degrees of freedom. For an infinite vortex crystal we compute how the Berry term affects the low-energy spectrum of soft collective Tkachenko oscillations and non-dissipative Hall responses of the particle number current and stress tensor. This term gives rise to a quadratic in momentum term in the Hall conductivity, but does not generate a non-dissipative Hall viscosity.