  At zero temperature, two-site dynamical mean field theory is applied to the
Dynamic Hubbard model. The Dynamic Hubbard model describes the orbital
relaxation that occurs when two electrons occupy the same site, by using a
two-level boson field at each site. At finite boson frequency, the appearance
of a Mott gap is found to be enhanced even though it shows a metallic phase
with the same bare on-site interaction $U$ in the conventional Hubbard model.
The lack of electron-hole symmetry is highlighted through the quasi-particle
weight and the single particle density of states at different fillings, which
qualitatively differentiates the dynamic Hubbard model from other conventional
Hubbard-like models.
