Spacetime symmetries of the quantum Hall effect

By M. Geracie, D. Son, Chaolun Wu, Shao-Feng Wu. 2014

181 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/53831b93b92c127495b44c5936b409bfd2d0694d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Torsional Newton–Cartan geometry and the Schrödinger algebra (2014, background): “Around the same time the works [32, 33, 34, 35, 36, 37, 38, 39, 40, 41] appeared in which field theories coupled to TNC geometries are studied2.”
Gauging the Carroll algebra and ultra-relativistic gravity (2015, background): “In the case of field theory on Newton-Cartan space-times including torsion is crucial because it allows one to compute the energy current [1, 16, 17, 19, 23].”
On the coupling of Galilean-invariant field theories to curved spacetime (2014, methodology): “Most recently in [6], Son and collaborators have derived the infinitesimal transformations so that the theory with gs is invariant under reparameterizations of space and time.”
Lifshitz holography (2015, background): “For example, TTNC has been proposed to be relevant to condensed matter physics, in the context of an effective field theory for the fractional quantum Hall effect, see [144, 145].”
Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry (2015, methodology): “Later torsion was added to this analysis in [26].”
Lifshitz space–times for Schrödinger holography (2014, background): “[23, 24, 25, 26, 27] following the earlier work [28] that introduced NC geometry to this problem).”