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- Synthetic non-Abelian anyons in fractional Chern insulators and beyond

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PIRSA Number:

12100051

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.

©2012 Institut Périmètre de Physique Théorique