A metal-insulator transition as a quantum glass problem

Details A metal-insulator transition as a quantum glass problem A metal-insulator transition as a quantum glass problem

1996-09-23

arxiv.org/abs/cond-mat/9609221v2

M. Rubi and C. Perez-Vicent (eds.), `Complex Behaviour of Glassy Systems', Lecture Notes in Physics vol. 492 (Springer, Berlin

Physics

Condensed Matter

Statistical Mechanics

10 pp., REvTeX, 1 eps fig., Sitges Conference Proceedings, final version as published

Scientific paper

10.1007/BFb0104831

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.

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