Strong Disorder RG approach - a short review of recent developments

TL;DR

This review summarizes recent advancements in the Strong Disorder Renormalization Group (RG) approach across quantum and classical disordered systems, highlighting new theoretical developments, applications, and understanding of complex phenomena.

Contribution

It provides a comprehensive overview of recent extensions and applications of the Strong Disorder RG method in diverse disordered models since 2005.

Findings

Progress in Infinite Disorder Fixed Points for higher-dimensional models

Development of RSRG-X and RSRG-t procedures for excited states and dynamics

Applications to classical models like epidemic spreading and oscillator synchronization

Abstract

The Strong Disorder RG approach for random systems has been extended in many new directions since our previous review of 2005 [Phys. Rep. 412, 277]. 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.