L-8

Goal: we will introduce the Anderson model, discuss the behaviour as a function of the dimension. In 1d localization can be connected to the product of random matrices.

Anderson model (tight bindind model)

We consider a lattice with non-interacting particles hopping between nearest neighbors and feeling on-site disorder. The hamiltonian reads:

$H=-t\sum _{<i,j>}(c_{i}c_{j}+c_{j}c_{i})\sum _{i}\epsilon _{i}c_{i}c_{i}$