Fractional quantum Hall effect in a relativistic field theory

TL;DR

This paper constructs relativistic quantum field theories in 2+1 dimensions that exhibit the Fractional Quantum Hall Effect, revealing topological phases with fractional charges and anyonic excitations in both continuum and lattice settings.

Contribution

It introduces a UV-complete relativistic field theory model that realizes fractional quantum Hall states with novel topological features.

Findings

Realization of fractional quantum Hall states in relativistic field theories

Presence of fractional charges and anyonic excitations

Potential for exotic phenomena like fractional quantum spin Hall effect

Abstract

We construct a class of 2+1 dimensional relativistic quantum field theories which exhibit the Fractional Quantum Hall Effect in the infrared, both in the continuum and on the lattice. The UV completion consists of a perturbative $U(1)\times U(1)$ gauge theory with only integer-charged fields, while the low energy spectrum consists of nontrivial topological phases supporting fractional currents, fractionally charged chiral surface modes and bulk anyonic excitations. Exotic phenomena such as a Fractional Quantum Spin Hall Effect can arise in such models.