Quasiparticles in a Bose-Fermi mixture in optical lattice

We investigate a mixture of interacting bosons and fermions using a generalized dynamical mean-field theory combined with the numerical renormalization group. We focus on many-body effects in the presence of the superfluidity. It is elucidated that fermionic particles are strongly renormalized by low-energy bosonic excitations via the boson-fermion interaction, giving rise to an anomalous peak structure in the density of states for fermions. We also address how the renormalization effects appear in the phases with long-range order such as a supersolid phase.