A universal description of Mott insulators: Characterizing quantum phases beyond broken symmetries

Using Mott insulators as a prototypical example, we demonstrate a dynamics-based characterization of quantum phases of matter through a general N-body renormalization group framework. The essential "Mott-ness" turns out to be characterized by a change of size-scaling of the effective intra-momentum repulsions between long-lived emergent "eigen-particles" that encodes the dynamics of two-body bound states in the high-energy sector. This directly offers a universal characterization at long space-time scale for the corresponding class of Mott insulators through a uniform single occupation of all momenta, and otherwise Mott metals. This universal description naturally paves the way to topological Mott insulators and is straightforward to extend to bosonic Mott systems. More generally, this demonstration exemplifies a generic paradigm of characterizing quantum phases of matter through their distinct dynamics beyond broken symmetries.