The localization frontier---from many-body localization to amorphous topological matter via the landscape
The last decade has seen impressive progress in the control and understanding of closed many-body quantum systems, propelled by the drive towards quantum technology. This progress, especially in understanding nonequilibrium many-body quantum dynamics, is now severely hampered by the limited toolbox available for studying such systems. This is especially true in systems far from their absolute zero temperature ground states and where disorder or imperfections play a crucial role. Such systems are at the core of some of the most fundamental open questions in quantum physics, including how and when such systems become thermal and behave according to classical expectations, and when they do not. The many-body localization transition is a poorly understood, unconventional dynamic phase transition that is believed to prevent many-body quantum systems form thermalizing. The underlying mechanism for this transition is localization of particles due to quantum interference induced by scattering of imperfections. As a result of the localization, quantum information that otherwise would become inaccessible due to thermalization, can in principle be retained indefinitely.  The major objective of this project is to significantly enhance and enlarge the toolbox for study of quantum-many body dynamics and localization physics in general, and by applying the new tools address open fundamental questions about quantum physics. The problem is hard, and most approaches to new tools are at the outset likely to fail. The project therefore takes a multipronged approach by developing several new methods in addition to improving and applying old ones in new directions. This includes conceptually new approaches to localization (the localization landscape), inspired by recent advances in mathematics, which will be broadly applicable to localization physics in general. This broad applicability will be demonstrated by also applying it to the physics of amorphous topological matter.