Self-consistent theory of mobility edges in quasiperiodic chains

We introduce a self-consistent theory of mobility edges in nearest-neighbor tight-binding chains with quasiperiodic potentials. Demarcating boundaries between localized and extended states in the space of system parameters and energy, mobility edges are quite typical in quasiperiodic systems which lack the energy-independent self-duality of the commonly studied Aubry-Andr\'e-Harper model. The potentials in such systems are strongly and infinite-range correlated, reflecting their deterministic nature and rendering the problem distinct from that of disordered systems. Importantly, the underlying theoretical framework introduced is model independent, thus allowing analytical extraction of mobility edge trajectories for arbitrary quasiperiodic systems. We exemplify the theory using two families of models and show the results to be in very good agreement with the exactly known mobility edges as well as numerical results obtained from exact diagonalization.