First I will discuss the Eigenstate Thermalization Hypothesis (ETH), which appears to be true for the broad class of many-body quantum systems that function as heat baths and thermally equilibrate themselves under the dynamics given by their own Hamiltonian.  The one generic exception to ETH that is known is many-body Anderson localization.  We have studied a model spin chain that shows both thermalizing and localized phases, with a dynamic quantum phase transition between them that occurs even at arbitrarily high temperature.  I will highlight some of the many important differences between the two phases and describe some of our results that (roughly) locate the phase transition and constrain some of its properties.

Work in collaboration with Arijeet Pal and Vadim Oganesyan.