Finite-size effects in Anderson localization of one-dimensional Bose-Einstein condensates

TL;DR

This paper studies how finite system size affects the localization transition in one-dimensional Bose-Einstein condensates under disorder, using exact diagonalization and various indicators like entanglement and fidelity.

Contribution

It introduces finite-size scaling laws for the critical disorder strength and demonstrates the effectiveness of fidelity as a sensitive indicator in small systems.

Findings

Fidelity is highly sensitive to localization transition even in small lattices.

Finite-size scaling laws for critical disorder strength are established.

Entanglement and superfluid fraction also signal the transition clearly.

Abstract

We investigate the disorder-induced localization transition in Bose-Einstein condensates for the Anderson and Aubry-Andre models in the non-interacting limit using exact diagonalization. We show that, in addition to the standard superfluid fraction, other tools such as the entanglement and fidelity can provide clear signatures of the transition. Interestingly, the fidelity exhibits good sensitivity even for small lattices. Effects of the system size on these quantities are analyzed in detail, including the determination of a finite-size-scaling law for the critical disorder strength in the case of the Anderson model.