A metal-insulator transition as a quantum glass problem
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.
Cite
@article{arxiv.cond-mat/9609221,
title = {A metal-insulator transition as a quantum glass problem},
author = {T. R. Kirkpatrick and D. Belitz},
journal= {arXiv preprint arXiv:cond-mat/9609221},
year = {2009}
}
Comments
10 pp., REvTeX, 1 eps fig., Sitges Conference Proceedings, final version as published