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Many body localization (MBL) represents a unique physical phenomenon,providing a testing ground for exploring thermalization, or more precisely itsfailure. Here we characterize the MBL phase geometrically by the many-bodyquantum metric (MBQM), defined in the parameter space of twist boundary. Wefind that MBQM scales linearly as a function of the inverse system length inthe MBL phase, and grows faster in the ergodic phase. We validate our theoryusing the disordered hardcore Bose-Hubbard model, and characterize the ergodicto MBL phase transition via the localization length scale defined from theMBQM. MBQM provides an intuitive and experimentally accessible method tocharacterize MBL phases.

Geometric Characterization of Many Body Localization