Journal
PHYSICAL REVIEW B
Volume 90, Issue 11, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.90.115132
Keywords
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Funding
- EPSRC [EP/I032487/1, EP/I031014/1]
- Clarendon Fund Scholarship
- Merton College Domus and Prize Scholarships
- University of Oxford
- Engineering and Physical Sciences Research Council [1106120, EP/I032487/1, EP/I031014/1, 1100699] Funding Source: researchfish
- EPSRC [EP/I032487/1, EP/I031014/1] Funding Source: UKRI
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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.
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