New Kinds of Quantum Statistics

Abstract

I review the quantum kinematics of identical particles, which suggests new possibilities, beyond bosons and fermions, in 2+1 dimensions; and how simple flux-charge constructions embody the new possibilities, leading to both abelian and nonabelian anyons. I briefly allude to experimental realizations, and also advertise a spinor construction of nonabelian statistics, that has a 3+1 dimensional extension.

Talk at Seminaire Poincare (Bourbaphy), Paris, December 2007. To be published in the Proceedings. 6 pages, 4 figures. v2: Minor typos corrected, figures redrawn. v3: 2 more minor typos. Argh

References in corpus (1)

• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state

Cited by in corpus (5)

• Quantization of the thermal Hall conductivity at small Hall angles
• Coherent propagation of quasiparticles in topological spin liquids at finite temperature
• Correlation holes and slow dynamics induced by fractional statistics in gapped quantum spin liquids
• Electron-Tunneling-Assisted Non-Abelian Braiding of Rotating Majorana Bound States
• Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a ${\mathbb{Z}}_2$ gauge theory in three dimensions