Exact Topological Flat Bands from Continuum Landau Levels
arXiv:1910.08429 · doi:10.1103/PhysRevA.101.013629
Abstract
We construct and characterize tight binding Hamiltonians which contain a completely flat topological band made of continuum lowest Landau level wavefunctions sampled on a lattice. We find an infinite family of such Hamiltonians, with simple analytic descriptions. These provide a valuable tool for constructing exactly solvable models. We also implement a numerical algorithm for finding the most local Hamiltonian with a flat Landau level. We find intriguing structures in the spatial dependence of the matrix elements for this optimized model. The models we construct serve as foundations for numerical and experimental studies of topological systems, both non-interacting and interacting.
arXiv comment6 pages, 4 figures
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Cited by in corpus (6)
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- Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
- Theory of Generalized Landau Levels and Implication for non-Abelian States
- Origin of band flatness and constraints of higher Chern numbers
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