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• W2115890402 abstract "We show that all the bands of the Hofstadter model on the torus have an exactly flat dispersion and Berry curvature when a special system size is chosen. This result holds for any hopping and Chern number. Our analysis therefore provides a simple rule for choosing a particularly advantageous system size when designing a Hofstadter system whose size is controllable, like a qubit lattice or an optical cavity array. The density operators projected onto the flat bands obey exactly the Girvin-MacDonald-Platzman algebra, like for Landau levels in the continuum in the case of $C=1$, or obey its straightforward generalization in the case of $C>1$. This allows a mapping between density-density interaction Hamiltonians for particles in the Hofstatder model and in a continuum Landau level. By using the well-known pseudopotential construction in the latter case, we obtain fractional Chern insulator phases, the lattice counterpart of fractional quantum Hall phases, that are exact zero-energy ground states of the Hofstadter model with certain interactions. Finally, the addition of a harmonic trapping potential is shown to lead to an appealingly symmetric description in which a new Hofstadter model appears in momentum space." @default.
• W2115890402 created "2016-06-24" @default.
• W2115890402 creator A5011405933 @default.
• W2115890402 creator A5034573184 @default.
• W2115890402 date "2014-09-18" @default.
• W2115890402 modified "2023-09-28" @default.
• W2115890402 title "Exact solutions of fractional Chern insulators: Interacting particles in the Hofstadter model at finite size" @default.
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• W2115890402 doi "https://doi.org/10.1103/physrevb.90.115132" @default.
• W2115890402 hasPublicationYear "2014" @default.
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