From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: Adiabatic continuity and orbital entanglement spectrum

摘要: The possibility of realizing lattice analogs fractional quantum Hall (FQH) states, so-called Chern insulators (FCIs), in nearly flat topological (Chern) bands has attracted a lot recent interest. Here, we make the connection between Abelian as well non-Abelian FQH states and FCIs more precise. Using gauge-fixed version Qi's Wannier basis representation band, demonstrate that interpolation several FCI obtained by short-range interactions spin-orbit-coupled kagome model, corresponding continuum is smooth: gap remains approximately constant extrapolates to finite value thermodynamic limit, while low-lying part orbital entanglement spectrum qualitatively unaltered. spectra also provide first glimpse edge physics via bulk-boundary correspondence. Corroborating these results, find squared overlaps ground are large $98.7%$ for 8-electron Laughlin state at $\ensuremath{\nu}=\frac{1}{3}$ (consistent with an earlier study) $97.8%$ 10-electron Moore-Read $\ensuremath{\nu}=\frac{1}{2}$. For bosonic adiabatic continuity shown hold, albeit somewhat smaller associated overlaps, etc. Although going Landau-level problem often smooth, show this not always case considering fermions filling fraction $\ensuremath{\nu}=\frac{4}{5}$, where Hamiltonians describing two systems results phase transition.