Renormalization group of topological scattering networks

TL;DR

This paper develops a real-space renormalization group method for topological scattering networks, enabling analysis of strong disorder effects and revealing how microscopic interactions lead to macroscopic topological phases.

Contribution

It introduces a novel RG scheme based on block-scattering and replica strategies for disordered systems, advancing understanding of topological phase transitions without relying on Hamiltonian renormalization.

Findings

Topological flow diagrams show competition between reflection and non-reciprocity.

Scaling analysis confirms critical exponents and localization length behavior.

Experimental validation supports the theoretical framework.

Abstract

Exploring and understanding topological phases in systems with strong distributed disorder requires developing fundamentally new approaches to replace traditional tools such as topological band theory. Here, we present a general real-space renormalization group (RG) approach for scattering models, which is capable of dealing with strong distributed disorder without relying on the renormalization of Hamiltonians or wave functions. Such scheme, based on a block-scattering transformation combined with a replica strategy, is applied for a comprehensive study of strongly disordered unitary scattering networks with localized bulk states, uncovering a connection between topological physics and critical behavior. Our RG scheme leads to topological flow diagrams that unveil how the microscopic competition between reflection and non-reciprocity leads to the large-scale emergence of macroscopic scattering attractors, corresponding to trivial and topological insulators. Our findings are confirmed by a scaling analysis of the localization length (LL) and critical exponents, and experimentally validated. The results not only shed light on the fundamental understanding of topological phase transitions and scaling properties in strongly disordered regimes, but also pave the way for practical applications in modern topological condensed-matter and photonics, where disorder may be seen as a useful design degree of freedom, and no longer as a hindrance.