Spacetime Symmetries of the Quantum Hall Effect
arXiv:1407.1252 · doi:10.1103/PhysRevD.91.045030
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.
31 pages
References in corpus (5)
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- Particle-hole symmetry and electromagnetic response of a half-filled Landau level
- Torsional Newton-Cartan Geometry and the Schrödinger Algebra
- Galilean invariance at quantum Hall edge
- Bosonic superfluid on lowest Landau level
- Renormalization properties of a Galilean Wess-Zumino model
- Holographic Hall conductivities from dyonic backgrounds
- Ward Identities for Hall Transport
- Uniqueness of Galilean Conformal Electrodynamics and its Dynamical Structure
- Electrons and composite Dirac fermions in the lowest Landau level
- Symmetries and Couplings of Non-Relativistic Electrodynamics
- Relativistic Gravity and Parity-Violating Non-Relativistic Effective Field Theories
- Developments in non-relativistic field theory and complexity