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Fractional Quantum Hall Effect in a Relativistic Field Theory
David B Kaplan1, Srimoyee Sen2
1Institute for Nuclear Theory, Box 351550, University of Washington, Seattle, Washington 98195-1550, USA.
Physical Review Letters
|April 18, 2020
Summary
This study constructs relativistic quantum field theories exhibiting the fractional quantum Hall effect. These theories feature fractional currents and anyonic excitations in their low-energy spectrum, demonstrating emergent fractional charge.
Area of Science:
- Condensed matter physics
- Quantum field theory
- Topological phases of matter
Background:
- The fractional quantum Hall effect (FQHE) is a key phenomenon in condensed matter physics, characterized by emergent fractional charges and exotic excitations.
- Understanding the theoretical underpinnings of FQHE, especially in relativistic settings and on lattices, remains an active area of research.
- Topological phases of matter offer a framework for describing exotic quantum phenomena beyond conventional Landau theory.
Purpose of the Study:
- To construct 2+1 dimensional relativistic quantum field theories that exhibit the fractional quantum Hall effect.
- To investigate the emergence of fractional currents, anyonic excitations, and the fractional quantum spin Hall effect in these theories.
- To demonstrate the explicit emergence of fractionally charged chiral edge states in the infrared (IR) limit.
Main Methods:
- Construction of 2+1 dimensional relativistic quantum field theories.
- Utilizing a perturbative U(1)×U(1) gauge theory with integer-charged fields for UV completion.
- Analysis of the low-energy spectrum to identify topological phases and emergent phenomena.
- Explicit derivation of fractionally charged chiral edge states.
Main Results:
- Successfully constructed relativistic quantum field theories exhibiting FQHE in both continuum and lattice formulations.
- Identified nontrivial topological phases in the low-energy spectrum.
- Observed fractional currents, bulk anyonic excitations, and a fractional quantum spin Hall effect.
- Explicitly demonstrated the emergence of fractionally charged chiral edge states in the infrared.
Conclusions:
- The developed framework provides a novel theoretical basis for understanding the fractional quantum Hall effect in relativistic systems.
- The findings highlight the rich emergent phenomena, including anyonic excitations and fractional spin Hall effect, present in these topological phases.
- The explicit construction of fractionally charged edge states offers insights into the topological nature of these quantum field theories.
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