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 integer-charged fields, while the low energy spectrum consists of nontrivial topological phases supporting fractional currents, bulk anyonic excitations, and exotic phenomena such as a fractional quantum spin Hall effect. We show explicitly how fractionally charged chiral edge states emerge in the IR.

• Received 6 December 2019
• Revised 6 February 2020
• Accepted 16 March 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.131601

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Published by the American Physical Society