TY - JOUR

T1 - Series of Abelian and non-Abelian states in C>1 fractional Chern insulators

AU - Sterdyniak, A.

AU - Repellin, C.

AU - Bernevig, B. Andrei

AU - Regnault, N.

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013/5/29

Y1 - 2013/5/29

N2 - We report the observation of a series of Abelian and non-Abelian topological states in fractional Chern insulators (FCIs). The states appear at bosonic filling ν=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 ground-state 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 ground-state 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 anomalies in the counting for C>1, possibly related to dislocations that call for the development of alternative counting rules of these topological states.

AB - We report the observation of a series of Abelian and non-Abelian topological states in fractional Chern insulators (FCIs). The states appear at bosonic filling ν=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 ground-state 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 ground-state 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 anomalies in the counting for C>1, possibly related to dislocations that call for the development of alternative counting rules of these topological states.

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U2 - 10.1103/PhysRevB.87.205137

DO - 10.1103/PhysRevB.87.205137

M3 - Article

AN - SCOPUS:84878529996

VL - 87

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 20

M1 - 205137

ER -