For irrational magnetic flux, the spectrum of the two-dimensional Hadamard magnetic quantum walk is a zero-measure Cantor set and the walk has no pure point spectrum, so the spectrum is purely singular continuous.
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Singular continuous Cantor spectrum for magnetic quantum walks
For irrational magnetic flux, the spectrum of the two-dimensional Hadamard magnetic quantum walk is a zero-measure Cantor set and the walk has no pure point spectrum, so the spectrum is purely singular continuous.