Feynman's Propagator Applied to Network Models of Localization

Abstract

Network models of dirty electronic systems are mapped onto an interacting field theory of lower dimensionality by intepreting one space dimension as time. This is accomplished via Feynman's interpretation of anti-particles as particles moving backwards in time. The method developed maps calculation of the moments of the Landauer conductance onto calculation of correlation functions of an interacting field theory of bosons and fermions. The resulting field theories are supersymmetric and closely related to the supersymmetric spin-chain representations of network models recently discussed by various authors. As an application of the method, the two-edge Chalker-Coddington model is shown to be Anderson localized, and a delocalization transition in a related two-edge network model (recently discussed by Balents and Fisher) is studied by calculation of the average Landauer conductance.

Latex, 14 pages, 2 figs

References in corpus (3)

• Delocalization Transition via Supersymmetry in one Dimension
• Scaling and Crossover Functions for the Conductance in the Directed Network Model of Edge States
• Conductance and its universal fluctuations in the directed network model at the crossover to the quasi-one-dimensional regime

Cited by in corpus (25)

• Anderson Transitions
• Delocalization in coupled one-dimensional chains
• Topology vs. Anderson localization: non-perturbative solutions in one dimension
• Density of states for the $\pi$-flux state with bipartite real random hopping only: A weak disorder approach
• Metal-insulator transition in 2D random fermion systems of chiral symmetry classes
• Dynamics and Transport in Random Antiferromagnetic Spin Chains
• The random magnetic flux problem in a quantum wire
• Crossover from the chiral to the standard universality classes in the conductance of a quantum wire with random hopping only
• The Chalker-Coddington Network Model is Quantum Critical
• Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid
• Statistical properties of localisation--delocalisation transition in one dimension
• Anisotropic Topological Anderson Transitions in Chiral Symmetry Classes
• Pseudo-Hermitian Hamiltonians Generating Waveguide Mode Evolution
• Dynamics and Critical Behaviour of the q-model
• Crossover of conductance and local density of states in a single-channel disordered quantum wire
• Dephasing catastrophe in $4-\epsilon$ dimensions: A possible instability of the ergodic (many-body-delocalized) phase
• Localized and Extended States in One-Dimensional Disordered System: Random-Mass Dirac Fermions
• Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry
• Nonlocally-Correlated Disorder and Delocalization in One Dimension: Density of States
• Nonlocally-correlated disorder and delocalization in one dimension II: Localization length
• Random-Mass Dirac Fermions in an Imaginary Vector Potential (I): Delocalization Transition and Localization Length
• Random-mass Dirac fermions in an imaginary vector potential: Delocalization transition and localization length
• Asymptotic behavior of the conductance in disordered wires with perfectly conducting channels
• Chiral chains with two valleys and disorder of finite correlation length
• Evading Anderson localization in a one-dimensional conductor with correlated disorder