H\"older mean applied to Anderson localization

TL;DR

This paper introduces a novel approach using the Hölder mean to analyze Anderson localization in disordered electron systems, revealing phase transitions and the effectiveness of different averaging methods in identifying localization.

Contribution

It applies the Hölder mean within dynamical mean-field theory to better understand phase diagrams and localization phenomena in correlated disordered systems.

Findings

Hölder mean effectively distinguishes between localized and delocalized phases.

Critical disorder strength is identified using this new averaging approach.

Different means (arithmetic, geometric) have specific roles in detecting Anderson localization.

Abstract

The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the H\"older mean local density of states. A critical disorder strength is determined in the Anderson-Falicov-Kimball model and the arithmetically and the geometrically averages are found to be just particular means used respectively to detect or not the Anderson localization. Correlated metal, Mott insulator and Anderson insulator phases, as well as coexistence and crossover regimes are analyzed in this new perspective.