Numerical methods 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.