Geometric Characterization of Many Body Localization

Abstract: Many body localization (MBL) represents a unique physical phenomenon, providing a testing ground for exploring thermalization, or more precisely its failure. Here we characterize the MBL phase geometrically by the many-body quantum metric (MBQM), defined in the parameter space of twist boundary. We find that we can characterise the transition by comparing the thermodynamic limits of the MBQM and localization length as defined in the modern theory of polarization and insulators. As such we find that we can extract a natural localization length in the MBL phase that relies only on the real space spread of the wave function and can be measured through lattice shaking or AC response measurements.