Zhao Liu, Emil J. Bergholtz
The possibility of realizing lattice analogues of fractional quantum Hall (FQH) states, so-called fractional Chern insulators (FCIs), in nearly flat topological (Chern) bands has attracted a lot of recent interest. Here, we make the connection between Abelian as well as non-Abelian fractional quantum Hall (FQH) states and fractional Chern insulators (FCIs) more precise. Using a gauge-fixed version of Qi's Wannier basis representation of a Chern band, we demonstrate that the interpolation between several FCI states, obtained by short-range lattice interactions in a spin-orbit coupled kagome lattice model, and the corresponding continuum FQH states is smooth: the gap remains approximately constant and extrapolates to a finite value in the thermodynamic limit, while the low lying part of the orbital entanglement spectrum remains qualitatively unaltered. Corroborating these results, we find that the squared overlaps between the FCI and FQH ground states are as large as 98.7% for the eight electron Laughlin state at $\nu=1/3$ and 97.8% for the ten electron Moore-Read state at $\nu=1/2$. For the bosonic analogues of these states, the adiabatic continuity is also shown to hold, albeit with somewhat smaller associated overlaps etc. We further provide an example where the interpolation between Hamiltonians of the two systems results in a phase transition by considering fermions at filling fraction $\nu=4/5$.
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http://arxiv.org/abs/1209.5310
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