Dynamics of quantum coherence in many-body localized systems

We demonstrate that the dynamics of quantum coherence serves as an effective probe for identifying dephasing, which is a distinctive signature of many-body localization (MBL). Quantum coherence can be utilized to measure both the local coherence of specific subsystems and the total coherence of the whole system in a consistent manner. Our results reveal that the local coherence of small subsystems decays over time following a power law in the MBL phase, while it reaches a stable value within the same time window in the Anderson-localized (AL) phase. In contrast, the total coherence of the whole system exhibits logarithmic growth during the MBL phase and reaches a stable value in the AL phase. Notably, this dynamic characteristic of quantum coherence remains robust even with weak interactions and displays unbounded behavior in infinite systems. Our results provide insights into understanding many-body dephasing phenomena in MBL systems and reveal a feasible method for identifying and characterizing MBL phases in experiments.