| Abstract: | It has been argued recently that closed quantum systems subject to strong enough quench disorder can become localized and fail to thermalize. In this talk I will discuss dynamics in the localized phase. I will show that rather than being a dead state, a many-body localized state can show universal dynamics and undergo transitions between distinct dynamical phases, characterized by a dynamical order parameter. The transition is described by a renormalization group approach which operates in real time, revealing the universal aspects and critical exponents of the transition. Finally, I will demonstrate that many-body localized systems can facilitate the existence of topological order in the entire many-body spectrum, rather than just the ground state. This leads to protected quantum bits even when the system is in a high energy state. |
