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 an ME which separates the localized and multifractal states in certain quasiperiodic systems, dubbed the anomalous mobility edges (AMEs). In this study, we propose a quasiperiodic system with solvable mobility edges that hosts both the conventional and anomalous mobility edges under proper conditions. We show that, with increase in quasiperiodic potential strength, the system first undergoes a delocalization to localization transition through an ME of conventional type. Surprisingly, with further increase in potential, we find 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 potential. 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 wave-packet dynamics.

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• Anderson localization
• Cold gases in optical lattices
• Localization
• Disordered systems