Fractional Quantum Hall Effect in a Relativistic Field Theory.

David B Kaplan,Srimoyee Sen

doi:10.1103/physrevlett.124.131601

David B Kaplan, Srimoyee Sen

Open Access

https://doi.org/10.1103/physrevlett.124.131601

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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)×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.

Highlights

Introduction.—Topological materials have been discussed in the context of lattice quantum field theories since the early 1990s
A field theoretic generalization of the TKNN calculation [6] was given in Ref. [7], where it was shown that the quantization of the CS operator coefficient had a topological origin, and that transitions between these topological phases were responsible for abrupt changes seen in the spectrum of chiral edge states [8]
Despite this long list of topological phases found in condensed matter that play a role in relativistic quantum field theory, notably missing to date is the fractional quantum Hall effect (FQHE)

Summary

Fractional Quantum Hall Effect in a Relativistic Field Theory

We construct a class of 2 þ 1 dimensional relativistic quantum field theories which exhibit the fractional quantum Hall effect in the infrared, both in the continuum and on the lattice. Examples of the SQHE seen experimentally [10,11], less trivial examples of anomaly cancellation have been studied numerically [9].) In yet another correspondence between relativistic and condensed matter topological materials, Majorana fermion edge states were introduced in the relativistic context [12] and used for the numerical simulation of gauginos in supersymmetric gauge theory [13], analogous to the Majorana modes of condensed matter systems [14] Despite this long list of topological phases found in condensed matter that play a role in relativistic quantum field theory, notably missing to date is the fractional quantum Hall effect (FQHE).

Published by the American Physical Society

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