On the spectrum of magnetic Laplacian on the Lieb lattice

2024/01/21 by Solis, Moises Gomez, Spedale, Dylan, Yang, Fan
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2401.11405

Abstract

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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