Hall viscosity, spin density, and torsion

TL;DR

The paper addresses whether torsion response can universally encode Hall viscosity and orbital spin in gapped systems. It analyzes general EFTs with torsion, free Dirac fields, relativistic quantum Hall setups, and non-relativistic Newton–Cartan theories, deriving torsion currents and viscosity contributions. The main result is that non-universal torsion couplings generically break the η_H–⟨ℓ⟩ relation and decouple torsion response from the spin density, while in relativistic theories the Hall viscosity arises only from the Euler current term and vanishes in Lorentz-invariant vacua. This work cautions against inferring orbital spin or Hall viscosity from torsion response and clarifies the precise geometric pathways by which Hall viscosity can appear in relativistic contexts.

Abstract

We investigate the relationship between Hall viscosity, spin density and response to geometric torsion. For the most general effective action for relativistic gapped systems, the presence of non-universal terms implies that there is no relationship between torsion response and Hall viscosity. We also consider free relativistic and non-relativistic microscopic actions and again verify the existence of analogous non-universal couplings. Explicit examples demonstrate that torsion response is unrelated to both Hall viscosity and spin density. We also argue that relativistic gapped theories must have vanishing Hall viscosity in Lorentz invariant vacuums.

Figures (1)

• Figure 1: Examples of lattice defects in two dimensional lattices, following Hughes:2012vg. On the left, we can see a dislocation defect and a non-zero Burgers vector in blue. On the right we have a disclination defect which can be seen from the parallel transport of the frame around the loop.