Field theory of Anderson transitions reviewed: Color-Flavor Transformation

Abstract: This talk is in two parts. First, the field-theoretic approach to (de-)localization in Anderson-type models for disordered electrons is reviewed, with emphasis placed on the presence of a hyperbolic target-space sector and the expected pattern of spontaneous symmetry breaking. The second part is a review of the "Color-Flavor (CF) Transformation" (MZ, 1996). Conceived as a variant of the Efetov-Wegner supersymmetry method, the CF Transformation is tailored to quantum systems with disorder distributed according to Haar measure for any compact Lie group of classical type (A, B, C, or D). It has been applied to Dyson's Circular Ensembles, random-link network models, quantum chaotic graphs, disordered Floquet dynamics, and more. It is reviewed here as a rigorous tool to derive the effective field theory for systems in the metallic regime.

mathematical physics

Audience: researchers in the discipline

( video )

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