Effective field theory of relativistic quantum hall systems

Abstract

Motivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. We find that, beside the Chern-Simons term, the effective action also contains a term of topological nature, which couples the electromagnetic field with a topologically conserved current of 2 + 1 dimensional relativistic fluid. In contrast to the Chern-Simons term, the new term involves the spacetime metric in a nontrivial way. We extract the predictions of the effective theory for linear electromagnetic and gravitational responses. For fractional quantum Hall states at the zeroth Landau level, additional holomorphic constraints allow one to express the results in terms of two dimensionless constants of topological nature.

The Euler current and relativistic parity odd transport

“…While the standard Chern-Simons term is Lorentz invariant, the mixed Wen-Zee term presents a problem since the (2 + 1) spin connection ω µ is a nonabelian connection, unlike the 1+1 dimensional version. Recently, we have found a relativistic version of the Wen-Zee term [14]; in this work we expand on the treatment of ref. [14] and extend the formalism to superfluids.…”

“…Recently, we have found a relativistic version of the Wen-Zee term [14]; in this work we expand on the treatment of ref. [14] and extend the formalism to superfluids.…”

“…In section 2 we define this new current and discuss its various properties. In section 3 we discuss coupling the Euler current to the relativistic quantum Hall EFT, summarizing and expanding on the results of [14]. In section 4 we discuss the dual description of the superfluid EFT and its coupling to the 1 While the massless Dirac cones have a Lorentz symmetry the sound speed is not the speed of light.…”

“…In this section we review the and expand on the results of [14]. As discussed in [14], the inclusion of the topological current is required to match the correct degeneracy of the Landau levels similar to the Wen-Zee term in the non-relativistic case.…”

“…As discussed in [14], the inclusion of the topological current is required to match the correct degeneracy of the Landau levels similar to the Wen-Zee term in the non-relativistic case. Our goal is to construct an effective field theory to describe Lorentz invariant quantum Hall systems after all heavy degrees of freedom have been integrated out, and we are left with a generating functional…”