Critical exponents of the disorder-driven superfluid-insulator   transition in one-dimensional Bose-Einstein condensates
  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. 
J. C. C. Cestari, A. Foerster, M. A. Gusm\~ao, M. Continentino
cond-mat.stat-mech cond-mat.quant-gas