Hall viscosity from effective field theory

TL;DR

This paper uses effective field theory to demonstrate that two-dimensional non-dissipative fluids with broken parity inherently exhibit Hall viscosity, linking it to angular momentum density and revealing unique sound wave polarization effects.

Contribution

It provides a relativistic effective field theory derivation of Hall viscosity and its relation to angular momentum, including novel predictions about sound wave polarization.

Findings

Hall viscosity is generically present in such fluids.

Hall viscosity equals the ground state's angular momentum density.

Sound waves exhibit elliptical polarization with frequency-dependent transverse-to-longitudinal ratio.

Abstract

For two-dimensional non-dissipative fluids with broken parity, we show via effective field theory methods that the infrared dynamics generically exhibit Hall viscosity--a conservative form of viscosity compatible with two-dimensional isotropy. The equality between the Hall viscosity coefficient and the ground state's intrinsic angular momentum density follows straightforwardly from their descending from the same Lagrangian term of the low-energy effective action. We show that for such fluids sound waves are not purely longitudinal, but acquire an elliptical polarization, with transverse-to-longitudinal aspect ratio proportional to frequency. Our analysis is fully relativistic, thus providing a natural description of (2+1) dimensional relativistic fluids with broken parity.