Anderson localization on a simplex

TL;DR

This paper develops an exact field-theoretical approach to analyze eigenstate localization in the generalized Anderson model, demonstrating that in the simplex model, eigenstates are localized regardless of disorder strength, with results confirmed numerically.

Contribution

It introduces an exact field-theoretical method applicable to the Anderson model with non-random hopping in any dimension, specifically analyzing the simplex model.

Findings

Eigenstates are localized at all disorder strengths in the simplex model.

Analytical predictions match numerical simulations.

The method applies broadly to models with non-random hopping.

Abstract

We derive a field-theoretical representation for the moments of the eigenstates in the generalized Anderson model. The representation is exact and can be used for the Anderson model with generic non-random hopping elements in any dimensions. We apply this method to the simplex model, for which the hopping amplitude between any two lattice sites is the same, and find that the eigenstates are localized at any strength of disorder. Our analytical predictions are in excellent agreement with the results of numerical simulations.