. . . To encourage the growth of any science, the best thing we can do is to meet together in its interest, to discuss its problems, to criticize each other's work and, best of all, to provide means by which the better portion of it may be made known to the world. . . .
In this work, we propose new symmetry-enriched topological states, topological nematic states, which are a dramatic consequence of the interplay between the lattice translation symmetry and fractional Quantum Hall States realized in lattice models. When a partially filled flat band has a Chern number N, it can be mapped to an N-layer quantum Hall system. In such a system, we find that lattice dislocations can act as wormholes connecting the different layers and effectively change the topology of the space. Lattice dislocations become defects with non-trivial quantum dimension, even when the FQH state being realized is by itself Abelian. Our proposal leads to the possibility of realizing the physics of topologically ordered states on high genus surfaces in the lab even though the sample has only the disk geometry.
Reference: Maissam Barkeshli and Xiao-Liang Qi, arxiv:1112.3311