Phase transition in a Aubry-Andre system with rapidly oscillating magnetic field

TL;DR

This paper explores a modified Aubry-Andre model with a rapidly oscillating magnetic field, revealing an energy-dependent mobility edge and potential experimental realization in optical lattices.

Contribution

It introduces a high-frequency oscillatory magnetic field to the Aubry-Andre model, resulting in an effective Hamiltonian with unique localization properties and an energy-dependent mobility edge.

Findings

Effective Hamiltonian retains tri-diagonal form.

Presence of an energy-dependent mobility edge.

Potential for experimental realization in optical lattices.

Abstract

We investigate a variant of the Aubry-Andr\'e-Harper (AAH) model corresponding to a bosonic optical lattice of ultra cold atoms under an effective oscillatory magnetic field. In the limit of high frequency oscillation, the system maybe approximated by an effective time independent Hamiltonian. We have studied localization/delocalization transition exhibited by the effective Hamiltonian. The effective Hamiltonian is found to retain the tight binding tri-diagonal form in position space. In a striking contrast to the usual AAH model, this non-dual system shows an energy dependent mobility edge - a feature which is usually reminiscent of Hamiltonians with beyond the nearest neighbour hoppings in real space. Finally, we discuss possibilities of experimentally realizing this system in optical lattices.