Development of long-range phase coherence on the Kondo lattice

Despite of many efforts, we still lack a clear picture on how heavy electrons emerge and develop on the Kondo lattice. Here we introduce a key concept named the hybridization bond phase and propose a scenario based on phase correlation to address this issue. The bond phase is a gauge-invariant quantity combining two onsite hybridization fields mediated by inter-site magnetic correlations. Its probabilistic distribution decays exponentially with site distance, from which a characteristic length scale can be extracted to describe the spatial correlation of Kondo hybridizations. Our calculations show that this correlation length grows logarithmically with lowering temperature at large Kondo coupling, and reveal a precursor pseudogap state with short-range phase correlation before long-range phase coherence is developed to form the Kondo insulating (or heavy electron) state at low temperatures. This provides a potential microscopic explanation of the two-stage hybridization proposed by recent pump-probe experiment and the logarithmic scaling in the phenomenological two-fluid model. Our work offers a novel theoretical framework to describe the phase-related physics in Kondo lattice systems.