The Anderson-Mott transition

TLDR

The review discusses key physical ideas and phenomenological approaches to the metal‑insulator transition and related phase‑transition problems such as disordered superconductors and the quantum Hall effect. The authors aim to review the interacting disordered electron problem, emphasizing quantum phase transitions in a model system and the field‑theoretic methods used to describe them. They develop an extended nonlinear sigma model as an effective field theory, derive a general scaling theory of metal‑insulator transitions, and compare renormalization‑group calculations across universality classes with experimental results, while also addressing conservation laws, diffusive dynamics, and phenomenological approaches to related problems. The review presents a scaling theory of metal‑insulator transitions, compares its predictions with experiments, and concludes by outlining open problems.

Abstract

The interacting disordered electron problem is reviewed with emphasis on the quantum phase transitions that occur in a model system and on the field-theoretic methods used to describe them. An elementary discussion of conservation laws and diffusive dynamics is followed by a detailed derivation of the extended nonlinear sigma model, which serves as an effective field theory for the problem. A general scaling theory of metal-insulator and related transitions is developed, and explicit renormalization-group calculations for the various universality classes are reviewed and compared with experimental results. A discussion of pertinent physical ideas and phenomenological approaches to the metal-insulator transition not contained in the sigma-model approach is given, and phase-transition aspects of related problems, like disordered superconductors and the quantum Hall effect, are discussed. The review concludes with a list of open problems.