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A metal-insulator transition as a quantum glass problem

T. R. Kirkpatrick·D. Belitz
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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.

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T. R. Kirkpatrick, D. Belitz. 1999-12-22. A metal-insulator transition as a quantum glass problem. https://doi.org/10.1007/bfb0104831

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