On the spectrum of magnetic Laplacian on the Lieb lattice
We study the magnetic Laplacian on the Lieb lattice, and prove Cantor spectrum for arbitrary irrational magnetic flux. We also provide a complete spectral analysis for the reduced one-dimensional Hamiltonian, proving Cantor spectra for all irrational frequencies, and sharp arithmetic phase transitions. Part of our analysis reveals a novel coexistence phenomenon of point spectrum and absolutely/singular continuous spectrum.
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