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arXiv · 1207.6385

Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators

A. Sterdyniak·C. Repellin·B. Andrei Bernevig·N. Regnault
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Abstract

We report the observation of a new series of Abelian and non-Abelian topological states in fractional Chern insulators (FCI). The states appear at bosonic filling nu= k/(C+1) (k, C integers) in several lattice models, in fractionally filled bands of Chern numbers C>=1 subject to on-site Hubbard interactions. We show strong evidence that the k=1 series is Abelian while the k>1 series is non-Abelian. The energy spectrum at both groundstate filling and upon the addition of quasiholes shows a low-lying manifold of states whose total degeneracy and counting matches, at the appropriate size, that of the Fractional Quantum Hall (FQH) SU(C) (color) singlet k-clustered states (including Halperin, non-Abelian spin singlet states and their generalizations). The groundstate momenta are correctly predicted by the FQH to FCI lattice folding. However, the counting of FCI states also matches that of a spinless FQH series, preventing a clear identification just from the energy spectrum. The entanglement spectrum lends support to the identification of our states as SU(C) color-singlets but offers new anomalies in the counting for C>1, possibly related to dislocations that call for the development of new counting rules of these topological states.

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A. Sterdyniak, C. Repellin, B. Andrei Bernevig, N. Regnault. 2012-07-26. Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators. https://doi.org/10.1103/physrevb.87.205137

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