Looking into thermalization and localization through the lens of quantum coherence

Quantum coherence quantifies the amount of superposition a quantum state can have in a basis. Since there is a difference in the structure of eigenstates of the ergodic and many-body localized systems, we expect them also to differ in terms of their coherences. Here, we numerically calculate different measures of quantum coherence in the excited eigenstates of an interacting disordered Hamiltonian as a function of the disorder. We show that these can be used as an order parameter to detect the well-studied ergodic to the many-body localized phase transition. We also perform quantum quench studies to distinguish the behavior of coherence in thermalized and localized phases. We present a protocol to calculate measurement-based localized coherence to investigate the thermal and many-body localized phases. The protocol allows looking at the correlation in a non-destructive way since tracing out a subsystem always destroys coherence and correlation.