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Lattice models forming bands with nonzero Chern number offer an intriguing possibility for topological phases of matter, namely fractional Chern insulators (FCIs).
First, we establish the existence of a number of new FCI states, with no analogue in continuum Landau levels, at fractional filling in flat bands with Chern number C=N >1. In particular, we find compelling evidence for a series of stable states at ν=1/(2N+1) for fermions as well as bosonic states at ν=1/(N+1). By examining the topological ground state degeneracies and the excitation structure as well as the entanglement spectrum, we conclude that these states are Abelian. However, these states are nevertheless qualitatively different from conventional quantum Hall (multilayer) states due to the novel properties of the underlying band structure. Second, we establish the adibatic continuity from FCIs in C=1 band to Abelian and non-Abelian fractional quantum Hall states by the gauge-fixed Wannier mapping. Finally, we briefly demonstrate the density matrix renormalization group simulations of the FCI systems, also with the help of the Wannier mapping. |
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