Density of States near the Anderson Transition in a Space of Dimensionality d=4-epsilon

TL;DR

This paper provides asymptotically exact results for the density of states near the Anderson transition in a space of dimension 4 minus epsilon, using advanced perturbation theory and renormalization techniques.

Contribution

It introduces a novel analytical approach combining renormalizability and Lipatov asymptotics to analyze the density of states near the Anderson transition.

Findings

Exact results for Green function and density of states across energy range

Analysis includes the vicinity of the mobility edge

Method accounts for all powers of 1/epsilon in large N limit

Abstract

Asymptotically exact results are obtained for the average Green function and the density of states in a Gaussian random potential for the space dimensionality d=4-epsilon over the entire energy range, including the vicinity of the mobility edge. For N\sim 1 (N is an order of the perturbation theory) only the parquet terms corresponding to the highest powers of 1/epsilon are retained. For large N all powers of 1/epsilon are taken into account with their coefficients calculated in the leading asymptotics in N. This calculation is performed by combining the condition of renormalizability of the theory with the Lipatov asymptotics.