Feynman's Propagator Applied to Network Models of Localization

TL;DR

This paper introduces a novel method using Feynman's propagator concept to analyze network models of electronic localization, mapping them onto supersymmetric field theories to study conductance and localization transitions.

Contribution

It develops a new approach applying Feynman's interpretation to map network models onto supersymmetric field theories, enabling analysis of localization and delocalization transitions.

Findings

The two-edge Chalker-Coddington model is shown to be Anderson localized.

A delocalization transition is studied via Landauer conductance calculations.

The method connects network models with supersymmetric field theories.

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.