Many-body dynamical localisation of coupled quantum kicked rotors

TL;DR

This paper maps the quantum dynamics of coupled kicked rotors to an interacting Anderson model, revealing many-body localization phenomena in momentum space and discussing limitations due to the bounded energy spectrum.

Contribution

It establishes a novel mapping between coupled quantum kicked rotors and an interacting Anderson model, highlighting many-body localization in momentum space.

Findings

Mapping predicts many-body localized phases in momentum space.

Interactions do not destroy Anderson localization in the mapped system.

Bounded energy spectrum limits the class of models that can be mapped.

Abstract

The quantum motion of $N$ coupled kicked rotors is mapped to an interacting $N$-particle Anderson-Aubry-Andr$\'e$ tight-binding problem supporting many-body localised (MBL) phases. Interactions in configuration space are known to be insufficient for destroying Anderson localisation in a system in the MBL phase. The mapping we establish here predicts that a similar effect takes place in momentum space and determines the quantum dynamics of the coupled kicked rotors. Due to the boundedness of the Floquet quasi-energy spectrum there exists limitations on the interacting lattice models that can be mapped to quantum kicked rotors; in particular, no extensive observable can be mapped in the thermodynamic limit.