Quantum criticality at the Anderson transition: a TMT perspective

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.

12 pages, 9 figures

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Cited by in corpus (7)

• Disorder-driven metal-insulator transitions in deformable lattices
• Dynamical Mean-Field Theory of Strongly Correlated Electron Systems
• Real-space cluster dynamical mean-field approach to the Falicov-Kimball model: An alloy-analogy approach
• Ab initio typical medium theory of substitutional disorder
• Anderson localization effects on doped Hubbard model
• Non-local corrections to the typical medium theory of Anderson localization
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory