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Fractional Quantum Hall Effect in a Relativistic Field Theory.

David B Kaplan1, Srimoyee Sen2

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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.

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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.