Quantum criticality at the Anderson transition: a TMT perspective

TL;DR

This paper provides a comprehensive analytical and numerical analysis of the Typical Medium Theory for the Anderson transition, identifying universality classes and formulating an effective Landau theory for localization.

Contribution

It offers the first complete solution of TMT for the Anderson transition, including universality classes and a simplified critical behavior description.

Findings

Identified all universality classes within TMT.

Provided an effective Landau theory for Anderson localization.

Analyzed the impact of interaction-induced renormalizations.

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.