Abstract
 
Many-body localization is the suppression of transport in disordered, interacting systems. It is now clear that many realistic disordered spin and particle systems do possess such a phase and that this has profound implications for the system's dynamics. Recently, a characterization of the MBL phase has been proposed in terms of the existence of local integrals of motion. I will show how to build such local integrals of motion in perturbation theory in the interaction and how to find the phase boundaries.  If time allows, I will also comment on the implications of this work for the performance of the quantum adiabatic algorithm.
  Joint work with  M. Müller, V. Ros.