Random Walks and Anderson Localisation in a Three-Dimensional Class C Network Model

Abstract

We study the disorder-induced localisation transition in a three-dimensional network model that belongs to symmetry class C. The model represents quasiparticle dynamics in a gapless spin-singlet superconductor without time-reversal invariance. It is a special feature of network models with this symmetry that the conductance and density of states can be expressed as averages in a classical system of dense, interacting random walks. Using this mapping, we present a more precise numerical study of critical behaviour at an Anderson transition than has been possible previously in any context.

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• Review on Quantum Walk Computing: Theory, Implementation, and Application
• Anderson localization and the topology of classifying spaces
• Universal statistics of vortex lines
• Length Distributions in Loop Soups
• Universality classes of the Anderson transition in three-dimensional symmetry classes AIII, BDI, C, D and CI
• Optimized evolution of networks for principal eigenvector localization
• Quantum Network Models and Classical Localization Problems
• Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle
• Thermal quenches in the stochastic Gross-Pitaevskii equation: morphology of the vortex network
• Phase diagram of weak-magnetic-field quantum Hall transition quantified from classical percolation
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Spin quantum Hall effect and plateau transitions in multilayer network models
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes