  We construct a quasiperiodic lattice model in curved spacetime to explore the
crossover concerning both condensed matter and curved spacetime physics. We
study the related Anderson localization and find that the model has a clear
boundary of localized-extended phase separation, which leads to a swing
mobility edge, i.e., the coexistence of localized, swing and sub-extended
phases. The swing mobility edge, first reported here, features the
phase-dependent eigenstate, that is, the eigenstate swing between the extended
and localized state for differnt phase parameter of the quasiperiodic
potential. Furthermore, A novel self-consistent segmentation method is
developed to calculate the analytical expression of the critical point of phase
separation, and the rich phase diagram is obtained by calculating the fractal
dimension and scaling index in multifractal analysis.
