English

A metal-insulator transition as a quantum glass problem

Statistical Mechanics 2009-10-28 v2 Strongly Correlated Electrons

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.

Keywords

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

R2 v1 2026-07-22T11:54:42.568Z