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arXiv · 1411.4558

Quantum criticality at the Anderson transition: a TMT perspective

Samiyeh Mahmoudian·Shao Tang·Vladimir Dobrosavljević
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Abstract

We present a complete analytical and numerical solution of the Typical Medium Theory (TMT) for the Anderson metal-insulator transition. In this theory, we self-consistently calculate the typical amplitude of the electron wave-We present a complete analytical and numerical solution of the Typical Medium Theory (TMT) for the Anderson metal-insulator transition. This approach self-consistently calculates the typical amplitude of the electronic wave-functions, thus representing the conceptually simplest order-parameter theory for the Anderson transition. We identify all possible universality classes for the critical behavior, which can be found within such a mean-field approach. This provides insights into how interaction-induced renormalizations of the disorder potential may produce qualitative modifications of the critical behavior. We also formulate a simplified description of the leading critical behavior, thus obtaining an effective Landau theory for Anderson localization.

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Samiyeh Mahmoudian, Shao Tang, Vladimir Dobrosavljević. 2015-04-15. Quantum criticality at the Anderson transition: a TMT perspective. https://doi.org/10.1103/physrevb.92.144202

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