Localization in non-chiral network models for two-dimensional disordered wave mechanical systems

TL;DR

This paper investigates scattering network models for 2D disordered wave systems, analyzing universality classes, phase diagrams, and localization phenomena with numerical and theoretical insights.

Contribution

It introduces a comprehensive analysis of non-chiral network models for 2D disordered wave systems, including phase diagrams and localization properties, with numerical validation.

Findings

Identified critical points analogous to quantum Hall systems.

Calculated multifractal exponents and localization lengths.

Observed localization-delocalization transitions in spin 1/2 systems.

Abstract

Scattering theoretical network models for general coherent wave mechanical systems with quenched disorder are investigated. We focus on universality classes for two dimensional systems with no preferred orientation: Systems of spinless waves undergoing scattering events with broken or unbroken time reversal symmetry and systems of spin 1/2 waves with time reversal symmetric scattering. The phase diagram in the parameter space of scattering strengths is determined. The model breaking time reversal symmetry contains the critical point of quantum Hall systems but, like the model with unbroken time reversal symmetry, only one attractive fixed point, namely that of strong localization. Multifractal exponents and quasi-one-dimensional localization lengths are calculated numerically and found to be related by conformal invariance. Furthermore, they agree quantitatively with theoretical predictions. For non-vanishing spin scattering strength the spin 1/2 systems show localization-delocalization transitions.