| Sumario: | We introduce a self-consistent theory of mobility edges in nearest-neighbour
tight-binding chains with quasiperiodic potentials. Demarcating boundaries
between localised and extended states in the space of system parameters and
energy, mobility edges are generic 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
numerical results obtained from exact diagonalisation.
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