Effective Field Theory of the Random Flux Model

TL;DR

This paper develops a supersymmetric field theory framework for the random flux model, revealing universal long-range physics and supporting the existence of delocalized states in two dimensions, with extensions to non-Abelian cases.

Contribution

It introduces a supersymmetric non-linear sigma model description for the random flux model and its non-Abelian generalizations, advancing understanding of long-range correlations and delocalization.

Findings

Universal long-range physics described by the sigma model.

Evidence for delocalized states in 2D band center.

Long-range correlations in non-Abelian models for large N.

Abstract

The random flux model (defined here as a model of lattice fermions hopping under the influence of maximally random link disorder) is analysed field theoretically. It is shown that the long range physics of the model is described by the supersymmetric version of a field theory that has been derived earlier in connection with lattice fermions subject to weak random hopping. More precisely, the field theory relevant for the behaviour of n-point correlation functions is of non-linear sigma model type, where the group GL(n|n) is the global invariant manifold. It is argued that the model universally describes the long range physics of random phase fermions and provides further evidence in favour of the existence of delocalised states in the middle of the band in two dimensions. The same formalism is applied to the study of non-Abelian generalisations of the random flux model, i.e. N-component fermions whose hopping is mediated by random U(N) matrices. We discuss some physical applications of these models and argue that, for sufficiently large N, the existence of long range correlations in the band center (equivalent to metallic behaviour in the Abelian case) can be safely deduced from the RG analysis of the model.