  Recently, it has been suggested that the Many-Body Localized phase can be
characterized by local integrals of motion. Here we introduce a Hilbert space
preserving renormalization scheme that iteratively finds such integrals of
motion exactly. Our method is based on the consecutive action of a similarity
transformation using displacement operators. We show, as a proof of principle,
localization and the delocalization transition in interacting fermion chains
with random onsite potentials. Our scheme of consecutive displacement
transformations can be used to study Many Body Localization in any dimension,
as well as disorder-free Hamiltonians.
