PIRSA:12100051 Scientific Series Condensed Matter

DOI10.48660/12100051

Series: Quantum Matter

Qi, X. (2012). Synthetic non-Abelian anyons in fractional Chern insulators and beyond. Perimeter Institute. https://pirsa.org/12100051

Qi, Xiaoliang. Synthetic non-Abelian anyons in fractional Chern insulators and beyond. Perimeter Institute, Oct. 26, 2012, https://pirsa.org/12100051 

@misc{ pirsa_PIRSA:12100051,
  doi = {10.48660/12100051},
  url = {https://pirsa.org/12100051},
  author = {Qi, Xiaoliang},
  keywords = {Condensed Matter},
  language = {en},
  title = {Synthetic non-Abelian anyons in fractional Chern insulators and beyond},
  publisher = {Perimeter Institute},
  year = {2012},
  month = {oct},
  note = {PIRSA:12100051 see, \url{https://pirsa.org}}
}

Abstract

An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall states in simple lattice models without a large external magnetic field, which are called fractional Chern insulators. A fundamental question is whether qualitatively new states can be realized on the lattice as compared with ordinary fractional quantum Hall states. Here we propose new symmetry-enriched topological states, topological nematic states, which are a dramatic consequence of the interplay between the lattice translational symmetry and topological properties of these fractional Chern insulators. The topological nematic states are realized in a partially filled flat band with a Chern number N, which can be mapped to an N-layer quantum Hall system on a regular lattice. However, in the topological nematic states the lattice dislocations become non-Abelian defects which create "worm holes" connecting the effective layers, and effectively change the topology of the space. Such topology-changing defects, which we name as "genons", can also be defined in other physical systems. We develop methods to compute the projective non-abelian braiding statistics of the genons, and we find the braiding is given by  adiabatic modular transformations, or Dehn twists, of the topological state on the effective genus g surface. We find situations where the > genons have quantum dimension 2 and can be used for universal topological quantum computing (TQC), while the host topological state is by itself non-universal for TQC.

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