Complex many-particle systems ordinarily exhibit chaotic dynamics that rapidly scramble quantum information, and relax to a thermal equilibrium state described by familiar statistical mechanical principles. Strong disorder can dramatically change this outcome by pinning excitations that would carry heat, permanently preventing the system from relaxing to equilibrium -- a phenomena called "many-body localization" (MBL). MBL systems have quantum coherent dynamics even at high energy densities, raising the prospect of coherent quantum information storage, non-equilibrium topological states, and quantum criticality in "hot" matter without the need for cooling.
Thermalization and MBL represent two sharply distinct fates for macroscopic quantum systems, and are separated by a dynamical phase transition. This transition represents an entirely new kind of critical phenomena outside conventional thermal and quantum phase transitions. I will describe a new type of renormalization group approach that enables us to compute the universal scaling properties of this many-body (de)localization transition. I will also discuss how these properties can be measured experimentally in cold atom and trapped ion systems, in which MBL has recently been observed.