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We propose an energy-scale correspondence between the Mott physics and theKondo lattice physics and construct a tentative phase diagram of theircorrelated electrons with two characteristic energy scales $\omega^*$ and$\Omega$ marking the upper boundary of a low-energy regime with well-developedlong-range coherence and the lower boundary of localized spectral weight in theenergy space, respectively. In between, there exists a crossover region withemergent but damped quasiparticle excitations. We argue that the presence oftwo separate energy scales is a generic property of correlated electrons on alattice and reflects an intrinsic two-stage process of the quasiparticledynamics to build up the lattice coherence. For the Hubbard model, theycorrespond to the kink and waterfall structures on the dispersion, while forthe periodic Anderson model, they are associated with the indirect and directhybridization gaps. Our work reveals a deep connection between the Mott andKondo lattice physics and provides a basic ingredient for the study ofmany-body systems.

Energy-scale cascade and correspondence between Mott and Kondo lattice physics