Optical conductivity in the vicinity of a quantum critical point

We demonstrate an interrelation between the magnetic properties and optical conductivity σ(ω) for 3d electron systems with active orbital degree of freedom at a transition-metal ion: t_2g in d¹ and e_g in d⁷ configuration. Both systems are described within the two-band Hubbard model which we analyze using exact-diagonalization technique for a two-site molecule at quarter filling. We highlight the main features of the low-temperature optical conductivity spectra for e_g and t_2g electrons, in the presence of the crystal-field splitting and show that these spectra provide a way to determine both Hund’s exchange J_H and intraorbital Coulomb interaction U . The orbital polarization and the entanglement between spin and orbital degrees of freedom are also discussed, together with possible violations of the Goodenough-Kanamori rules.