Optical conductivity in dynamic Hubbard model

The Dynamic Hubbard model is a candidate to capture the physics of two-band Hubbard models, such as the enhancement of critical Hubbard $U$ for the Mott transition. A pseudo-spin $1/2$ auxiliary field, which modifies the Coulomb $U$ interaction based on the on-site occupancy of electrons, breaks the electron-hole symmetry normally associated with the Hubbard model. The dependence of optical conductivity on the number of particles also reveals the effect of the pseudo-spin on the spectral weight distribution as a function of frequency.