Strong disorder renormalization group primer and the superfluid-insulator transition

Abstract: This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of disordered-boson systems and the superfluid-insulator transition in one dimension. The fact that there is also a well understood weak disorder theory for this problem allows to illustrate what aspects of the physics change at strong disorder. In particular the strong disorder RG analysis suggests that the transitions at weak disorder and strong disorder belong to distinct universality classes, but this question remains under debate and is not fully resolved to date. Further applications of the strong disorder renormalization group to higher-dimensional Bose systems and to bosons coupled to dissipation are also briefly reviewed.