Friday, April 5, 2013

1304.1323 (Zhao Liu et al.)

Bulk-edge correspondence in fractional Chern insulators    [PDF]

Zhao Liu, D. L. Kovrizhin, Emil J. Bergholtz
It has been recently realised that strong interactions in topological Bloch bands can stabilise novel states of matter. In this paper we study connections between these systems namely fractional Chern insulators, and the fractional quantum Hall states in the cylinder geometry using a generalised gauge-fixed Wannier-Qi basis. This new setup offers important advantages compared to the earlier exact diagonalisation studies on a torus. Most notably, it gives access to the properties of edge states and to the single-cut orbital entanglement spectrum, hence to the physics of bulk-edge correspondence. In addition, it is readily implemented in the state-of-the-art density matrix renormalisation group algorithm, which allows for numerical simulations of significantly larger systems. We demonstrate our general approach on examples of flat-band models on Ruby and Kagome lattices at bosonic filling fractions $\nu=1/2$ and $\nu=1$, where we observe the signatures of (non)-Abelian phases and establish the correspondence between the physics of edge states and the entanglement in the bulk.
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