Mott Transitions in Topological Systems

Recent results relating to correlation-driven ("Mott" and "Wigner crystal") metal-insulator transitions in systems with non-negligible quantum geometry and band topology are reviewed. The extent to which concepts from topological transition in non-interacting systems may be carried over to Mott and similar transitions is considered and the relation of topological quantum numbers to Green function zeros and to edge states is discussed in the contexts of approximate analytical ("slave rotor") and numerical ("ghost Gutzwiller", density matrix renormalization group, dynamical mean field theory, quantum Monte Carlo) methods. Possible experimental realizations in bulk and Moire quantum materials are mentioned and future directions for research are outlined. My understanding of this subject owes a substantial debt to many colleagues and collaborators including Valentin Crepel, Stefan Divic, Michele Fabrizio,Antoine Georges, Daniele Guerci, Jed Pixley, Georgio Sangiovanni, Tomohiro Soejima, Patrick Tscheppe, Niklas Wagner, Timothy Wehling, Steven White and Yongxin Zeng.