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PIRSA:12100051

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https://pirsa.org/12100051

Synthetic non-Abelian anyons in fractional Chern insulators and beyond

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

Xiaoliang Qi Stanford University

Talk numberPIRSA:12100051
DOI10.48660/12100051
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

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.