On Many-Body Localization for Quantum Spin Chains
  For a one-dimensional spin chain with random local interactions, we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system. The construction uses a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors. 
John Z. Imbrie
math-ph cond-mat.dis-nn math.MP math.PR