Emergence of distinct exact mobility edges in a quasiperiodic chain

Mobility edges (MEs) constitute the energies separating the localized states from the extended ones in disordered systems. Going beyond this conventional definition, recent proposal suggests for an ME which separates the localized and multifractal states in certain quasiperiodic systems - dubbed as the anomalous mobility edges (AMEs). In this study, we propose an exactly solvable quasiperiodic system that hosts both the conventional and anomalous mobility edges under proper conditions. We show that with increase in quasiperiodic disorder strength, the system first undergoes a delocalization to localization transition through an ME of conventional type. Surprisingly, with further increase in disorder, we obtain that a major fraction of the localized states at the middle of the spectrum turn multifractal in nature. Such unconventional behavior in the spectrum results in two AMEs, which continue to exist even for stronger quasiperiodic disorder. We numerically obtain the signatures of the coexisting MEs complement it through analytical derivation using Avila's global theory. In the end we provide important signatures from the wavepacket dynamics.