Coexistence of distinct mobility edges in a 1D quasiperiodic mosaic model

We introduce a one-dimensional quasiperiodic mosaic model with analytically solvable mobility edges that exhibit different phase transitions depending on the system parameters. Specifically, by combining mosaic quasiperiodic next-nearest-neighbor hoppings and quasiperiodic on-site potentials, we rigorously demonstrate the existence of two distinct types of mobility edges: those separating extended and critical states, and those separating extended and localized states. Using Avila's global theory, we derive exact analytical expressions for these mobility edges and determine the parameter regimes where each type dominates. Our numerical calculations confirm these analytical results through fractal dimension analysis. Furthermore, we propose an experimentally feasible scheme to realize this model using Bose-Einstein condensates in optical lattices with engineered momentum-state transitions. We also investigate the effects of many-body interactions under mean-field approximation. Our work provides a fertile ground for studying the coexistence of different types of mobility edges in quasiperiodic systems and suggests a feasible experimental platform to observe and control these transitions.