Hidden localization transitions in generalized Aubry-Andr\'e models

TL;DR

This paper explores a generalized Aubry-Andr"e model revealing hidden localization transitions and unexpectedly linking these to massless Dirac fermions in curved spacetime, suggesting a novel connection between localization and analog gravity.

Contribution

It introduces a family of Hamiltonians generalizing Aubry-Andr"e models, uncovering hidden localization transitions and relating them to Dirac fermions in curved spacetime.

Findings

Hidden localization transitions occur in generalized Aubry-Andr"e models.

At the transition, the Hamiltonian matches that of a massless Dirac fermion in curved spacetime.

The phase transition is indicated by a zero in the normalized participation ratio.

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-Andr\'e model. Here, I consider a family of Hamiltonians that generalizes the Aubry-Andr\'e 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.