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Related Experiment Videos

Fractionalization, topological order, and quasiparticle statistics.

Masaki Oshikawa1, T Senthil

  • 1Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan.

Physical Review Letters
|April 12, 2006
PubMed
Summary

Topological order is crucial for fractionalization in gapped insulators. In 2D systems, fractional charge implies a minimum topological degeneracy, with quasiparticles requiring higher degeneracy.

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Area of Science:

  • Condensed matter physics
  • Topological phases of matter

Background:

  • Fractionalization describes the emergence of particles with charges that are fractions of the fundamental unit.
  • Gapped insulating phases are states of matter with an energy gap between the valence and conduction bands.

Purpose of the Study:

  • To establish the fundamental role of topological order in realizing fractionalization in gapped insulating phases.
  • To derive the relationship between topological degeneracy and fractional charge in two-dimensional systems.

Main Methods:

  • General theoretical principles are applied to analyze gapped insulating phases.
  • Topological properties, specifically degeneracy, are investigated in relation to fractionalization.

Main Results:

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  • Topological order is demonstrated to be essential for fractionalization in dimensions greater than or equal to two.
  • A minimum topological degeneracy, denoted as q(g), is derived for fractionalized charges in two-dimensional systems with genus g.
  • It is shown that if quasiparticles are bosons or fermions, the topological degeneracy must be at least q(2g).

Conclusions:

  • Topological order is a necessary condition for fractionalization in gapped insulators in d >= 2 dimensions.
  • The derived topological degeneracy provides a quantitative measure for fractionalization in two-dimensional systems.
  • The nature of quasiparticles (boson or fermion) imposes further constraints on the topological degeneracy.