Spacetime Symmetries of the Quantum Hall Effect

TL;DR

This paper explores the spacetime symmetries of non-relativistic quantum Hall systems, deriving Ward identities and connecting Hall viscosity with conductivity using Newton-Cartan geometry with torsion.

Contribution

It extends non-relativistic diffeomorphism invariance to full spacetime symmetry and develops a covariant formalism for analyzing quantum Hall effects.

Findings

Derived Ward identities from spacetime symmetries.

Demonstrated the smoothness of symmetries in the massless limit.

Reproduced known relations between Hall viscosity and conductivity.

Abstract

We study the symmetries of non-relativistic systems with an emphasis on applications to the fractional quantum Hall effect. A source for the energy current of a Galilean system is introduced and the non-relativistic diffeomorphism invariance studied in previous work is enhanced to a full spacetime symmetry, allowing us to derive a number of Ward identities. These symmetries are smooth in the massless limit of the lowest Landau level. We develop a formalism for Newton-Cartan geometry with torsion to write these Ward identities in a covariant form. Previous results on the connection between Hall viscosity and Hall conductivity are reproduced.