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

4 pages, REVTeX, 4 figures (postscript)

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Cited by in corpus (8)

• Random Network Models and Quantum Phase Transitions in Two Dimensions
• Unitary stochastic matrix ensembles and spectral statistics
• Wave-packet dynamics at the mobility edge in two- and three-dimensional systems
• Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder
• Renormalization group approach to energy level statistics at the integer quantum Hall transition
• From quantum graphs to quantum random walks
• Weakly chiral networks and 2D delocalized states in a weak magnetic field
• Real-space renormalization-group approach to the integer quantum Hall effect