Anderson localization and swing mobility edge in curved spacetime

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 subextended phases. The swing mobility edge reported here features the phase-dependent eigenstate, that is, the eigenstate swing between the extended and localized states for different phase parameters of the quasiperiodic potential. Furthermore, a 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.