Numerical methods for localization

TL;DR

This paper reviews numerical algorithms used to study Anderson localization, highlighting the challenges posed by randomness and the lack of symmetries in the Hamiltonian representation, and summarizes various approaches from different fields.

Contribution

It compiles and discusses various numerical methods specifically tailored for analyzing Anderson localization, emphasizing their development and application.

Findings

Numerical algorithms can effectively analyze Anderson localization despite randomness.

Different algorithmic approaches have been adapted from other fields for localization studies.

The paper provides a comprehensive overview of existing numerical techniques for localization.

Abstract

Anderson localization provides a challenge to numerical approaches due to the inherent randomness, and hence absence of simple symmetries, in its discrete Hamiltonian representation. Numerous algorithmic approaches have been developed or adopted from other fields and have been collected in this encyclopedia entry. In the discussions below, the emphasis is on the numerical algorithms for localization, while the discussion of the physics of localization is referred to in companion entries by Elgart and Oganesyan in this encyclopedia.