We study the spectrum and the density of states measure of the square Fibonacci Hamiltonian. We describe where the transitions from positive-measure to zero-measure spectrum and from absolutely continuous to singular density of states measure occur. This shows in particular that for almost every parameter from some open set, a positive-measure spectrum and a singular density of statesmeasure coexist. This provides the first physically relevant example exhibiting this phenomenon.
Cite this article
David Damanik, Anton Gorodetski, Spectral transitions for the square Fibonacci Hamiltonian. J. Spectr. Theory 8 (2018), no. 4, pp. 1487–1507DOI 10.4171/JST/232