Renormalization-group studies of disordered magnetic systems, strongly correlated electonic systems, and polymeric systems

Eamonn A. Campbell

Many of the most interesting electronic behaviours currently being studied are associated with strong correlations. In addition, many of these materials are disordered either intrinsically or due to doping. Solving interacting systems exactly is extremely computationally expensive, and approximate techniques developed for strongly correlated systems are not easily adapted to include disorder. As a non-interacting disordered model, it makes sense to consider the Anderson model as a first step in developing an approximate method of solution to the interacting and disordered Anderson-Hubbard model. Our renormalization group (RG) approach is modeled on that proposed by Johri and Bhatt [23]. We found an error in their work which we have corrected in our procedure. After testing the execution of the RG, we benchmarked the density of states and inverse participation ratio results against exact diagonalization. Our approach is significantly faster than exact diagonalization and is most accurate in the limit of strong disorder. Author Keywords: disorder, localization, real-space renormalization, strong correlations

Yixuan Huang

Taiki Haga

D. Mouhanna, Bertrand Delamotte, J.-P. Kownacki +1 more

The non-perturbative renormalization group (NPRG), in its modern form, constitutes an efficient framework to investigate the physics of systems whose long-distance behavior is dominated by strong fluctuations that are out of reach of perturbative approaches. We present here the basic principles underlying the NPRG and illustrate its power in the context of two longstanding problems of condensed matter and soft matter physics: the nature of the phase transition occuring in frustrated magnets in three dimensions and the phase diagram of polymerized phantom membranes.

Gil Refael, Ehud Altman

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 us 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.

Steven R. White