A metal-insulator transition as a quantum glass problem

TL;DR

This paper maps the Anderson-Mott metal-insulator transition onto a quantum glass problem, introducing an order parameter expansion approach and analyzing critical exponents through mean field and epsilon expansion methods.

Contribution

It presents a novel description of the metal-insulator transition using an order parameter expansion and connects it to random field magnet models, providing new insights into critical exponents.

Findings

Mean field theory yields exact critical exponents for d>6.

Epsilon expansion about d=6 matches random field Ising model exponents.

Dangerous irrelevant fluctuations alter Wegner's scaling law in d=3.

Abstract

We discuss a recent mapping of the Anderson-Mott metal-insulator transition onto a random field magnet problem. The most important new idea introduced is to describe the metal-insulator transition in terms of an order parameter expansion rather than in terms of soft modes via a nonlinear sigma model. For spatial dimensions d>6 a mean field theory gives the exact critical exponents. In an epsilon expansion about d=6 the critical exponents are identical to those for a random field Ising model. Dangerous irrelevant quantum fluctuations modify Wegner's scaling law relating the conductivity exponent to the correlation or localization length exponent. This invalidates the bound s>2/3 for the conductivity exponent s in d=3. We also argue that activated scaling might be relevant for describing the AMT in three-dimensional systems.