Condensed Matter Seminar - Prof Xiao-Liang Qi, Stanford University - "Synthetic non-Abelian anyons in fractional Chern insulators and beyond"
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.
Location: PCTS Seminar Room
Date/Time: 10/22/12 at 1:15 pm - 10/22/12 at 2:30 pm
Category: Condensed Matter Seminar