  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.
