Anderson Localization and Swing Mobility Edge in Curved Spacetime

TL;DR

This paper introduces a quasiperiodic lattice model in curved spacetime revealing a unique swing mobility edge where eigenstates transition between localized and extended states, enriching understanding of phase separation in such systems.

Contribution

It presents the first observation of a swing mobility edge in curved spacetime and develops a self-consistent segmentation method for analyzing phase transitions.

Findings

Identification of a clear boundary between localized and extended phases.

Discovery of the swing mobility edge with phase-dependent eigenstates.

Development of a novel analytical method for critical point calculation.

Abstract

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.