Anderson Localization and Mobility Edge in Curved Spacetime

We construct a quasiperiodic lattice model in a 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 the mobility edge, i.e., the coexistence of nonergodic localized, critical and extended phases. A novel self-consistent segmentation method is developed to calculate the analytical expression of the critical position of phase separation, and the rich phase diagram is determined by calculating the fractal dimension and scaling index in multifractal analysis.