Diagonalization and Many-Body Localization for a Disordered Quantum Spin   Chain
  We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of eigenvalues. In a KAM-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian by deforming the initial tensor product basis into a complete set of exact many-body eigenfunctions. 
John Z Imbrie
math-ph cond-mat.dis-nn math.MP math.SP