Possibility of the 2D Anderson Transition and Generalized Lyapunov Exponents

TL;DR

This paper investigates the potential for a 2D Anderson transition in non-interacting, spin-orbit-free systems by analyzing generalized Lyapunov exponents to clarify ongoing scientific debates.

Contribution

It provides a comparative analysis of approaches using generalized Lyapunov exponents to address the controversy over the 2D Anderson transition.

Findings

Analysis suggests conditions under which the 2D Anderson transition may occur.

Highlights the role of generalized Lyapunov exponents in understanding localization.

Clarifies conflicting results in previous studies.

Abstract

The possible existence of the Anderson transition in 2D systems without interaction and spin-orbit effects (such as the usual Anderson model) becomes recently a subject of controversy in the literature. Comparative analysis of approaches based on generalized Lyapunov exponents is given, in order to resolve controversy.