Approximating Metal-Insulator Transitions

TL;DR

This paper investigates quantum wave behavior in one-dimensional quasiperiodic lattices, proposing an iterative method to approximate metal-insulator transitions and revealing evidence of mobility edges differing from the Aubry-Andre model.

Contribution

It introduces a novel iterative construction of quasiperiodic potentials and demonstrates approximate metal-insulator transitions with evidence of mobility edges.

Findings

Observation of approximate MIT at finite iteration steps

Evidence of mobility edges differing from Aubry-Andre model

Critical slowing down of group velocity near MIT

Abstract

We consider quantum wave propagation in one-dimensional quasiperiodic lattices. We propose an iterative construction of quasiperiodic potentials from sequences of potentials with increasing spatial period. At each finite iteration step the eigenstates reflect the properties of the limiting quasiperiodic potential properties up to a controlled maximum system size. We then observe approximate metal-insulator transitions (MIT) at the finite iteration steps. We also report evidence on mobility edges which are at variance to the celebrated Aubry-Andre model. The dynamics near the MIT shows a critical slowing down of the ballistic group velocity in the metallic phase similar to the divergence of the localization length in the insulating phase.