Topology and exotic orders in quantum solids

Traditional Ginzburg-Landau paradigm successfully describes a large set of phenomena in solids. In this framework, phases of matter are ultimately characterized by emergent classical order parameters, even if the microscopic degrees freedom are quantum mechanical. However, recent experimental progresses in quantum solids force us to look into new patterns of emergence, or new types of orders, that are intrinsically quantum mechanical. I will firstly discuss the different types of topological phases in solids, including topological insulators, Weyl semimetals and fractional Chern insulators, together with their experimental signatures and (possible) realizations. I will then present our attempts to develop systematic theoretical frameworks to describe and to search these phases in strongly correlated materials.​