Critical exponents of the disorder-driven superfluid-insulator transition in one-dimensional Bose-Einstein condensates

TL;DR

This paper analyzes the critical behavior of the superfluid-insulator transition in one-dimensional Bose-Einstein condensates under disorder, using numerical scaling to determine quantum critical exponents for different disorder types.

Contribution

It provides the first detailed scaling analysis of the superfluid-insulator transition in 1D disordered BECs, comparing Anderson and Aubry-André models, and discusses interaction effects near criticality.

Findings

Determined quantum critical exponents for Anderson and Aubry-André models.

Identified differences in transition behavior between disorder types.

Briefly explored the influence of interactions near the critical point.

Abstract

We investigate the nature of the superfluid-insulator quantum phase transition driven by disorder for non-interacting ultracold atoms on one-dimensional lattices. We consider two different cases: Anderson-type disorder, with local energies randomly distributed, and pseudo-disorder due to a potential incommensurate with the lattice, which is usually called the Aubry-Andr\'e model. A scaling analysis of numerical data for the superfluid fraction for different lattice sizes allows us to determine quantum critical exponents characterizing the disorder-driven superfluid-insulator transition. We also briefly discuss the effect of interactions close to the non-interacting quantum critical point of the Aubry-Andr\'e model.