Hidden localization transitions in generalized Aubry-André models

Abstract: Anderson localization is a phase transition between a metallic phase, where wavefunctions are extended and delocalized in space, and an insulating phase, where wavefunctions are completely localized. These transitions are driven by uncorrelated disorder or quasiperiodic disorder, e.g., in the case of the Aubry-André model. Here, I consider a family of Hamiltonians that generalizes the Aubry-André model obtained when position and momentum operators are replaced by an arbitrary couple of canonically conjugate operators. In these models, a hidden localization transition occurs between metallic/insulating phases with wavefunctions delocalized/localized with respect to one of the two canonically conjugate operators. If the canonically conjugate operators coincide with a linear combination of position and momentum, the phase transition is signaled by a zero in the normalized participation ratio in the usual position space. Surprisingly, I found that at the phase transition, this model Hamiltonian coincides with the lattice Hamiltonian of a massless Dirac fermion in a curved spacetime background, indicating an unexpected relation between many-body localization and analog gravity.