Emergent Photons and Decaying Electrons: In Search of a New Paradigm for Quantum Materials Ashvin Vishwanath, Assistant Professor, Condensed Matter Theory Group, UC Berkeley

The conventional theory of solids that has enjoyed enormous successes in the last several decades is built on two fundamental paradigms: Landau's Fermi liquid theory and the Landau theory of phases and phase transitions, where the order parameter plays a central role. In recent years however a variety of correlated electronic systems have been discovered that seem to depart in fundamental ways from these paradigms. I will describe some theoretical ideas that have been put forward to resolve this impasse. Perhaps the most exciting of these are ideas that attribute the new physics to phases and phase transition that are described not in terms of a local order parameter, but in terms of a more subtle, global property - topological order. Such phases give rise to emergent gauge fields and excitations with fractional quantum numbers. They also allow for phenomena that were previously believed impossible - continuous transitions between certain phases and systematic violations of counting theorems like the Luttinger theorem.