Eur. Phys. J. B (2018) 91: 290
https://doi.org/10.1140/epjb/e2018-90434-8

Colloquium

Strong disorder RG approach – a short review of recent developments

¹ Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary
² Institute of Theoretical Physics, Szeged University, H-6720 Szeged, Hungary
³ Institut de Physique Théorique, Université Paris Saclay, CNRS, CEA, 91191 Gif-sur-Yvette, France

^a e-mail: igloi.ferenc@wigner.mta.hu
^b e-mail: cecile.monthus@cea.fr

Received: 3 July 2018
Received in final form: 26 August 2018
Published online: 21 November 2018

Abstract

The strong disorder RG approach for random systems has been extended in many new directions since our previous review of 2005 [F. Igloi, C. Monthus, Phys. Rep. 412, 277 (2005)]. The aim of the present colloquium paper is thus to give an overview of these various recent developments. In the field of quantum disordered models, recent progress concern infinite disorder fixed points for short-ranged models in higher dimensions d > 1, strong disorder fixed points for long-ranged models, scaling of the entanglement entropy in critical ground-states and after quantum quenches, the RSRG-X procedure to construct the whole set excited stated and the RSRG-t procedure for the unitary dynamics in many-body-localized phases, the Floquet dynamics of periodically driven chains, the dissipative effects induced by the coupling to external baths, and Anderson Localization models. In the field of classical disordered models, new applications include the contact process for epidemic spreading, the strong disorder renormalization procedure for general master equations, the localization properties of random elastic networks, and the synchronization of interacting non-linear dissipative oscillators. Application of the method for aperiodic (or deterministic) disorder is also mentioned.