There is also a new method which gets a hold of eigenvectors directly by an iterative diagonalization procedure rather than indirectly via expectations of products of resolvents. It is in the recent article "Multi-Scale Jacobi Method for Anderson Localization" by John Imbrie.

There is also a new method which gets a hold of eigenvectors directly by an iterative diagonalization procedure rather than indirectly via expectations of products of resolvents. It is in the recent article "Multi-Scale Jacobi Method for Anderson Localization" by John Imbrie.

I should add that the hot topic in the area now is many-body localization with tons of physics articles posted on the cond-mat section of arXiv. The above article by Imbrie can serve as an introduction to his other one about MBL: "On many-body localization for quantum spin chains" in JSP 2016.