The competition between the Ruderman-Kittel-Kasuya-Yosida effect and Kondo effect is a central subject of periodic Anderson model. By employing the density matrix embedding theory , we study a three orbital periodic Anderson model, in which the effects of degenerate conduction orbitals via the local magnetic moments, number of electrons, and spin-spin correlation functions, are investigated. From the phase diagram at half filling, we find there exist two different anti-ferromagnetic phases and one para-magnetic phase. To explore the difference of the two anti-ferromagnetic phases, the topology of Fermi surface and the connection with standard periodic Anderson model are considered. The spin-spin correlation functions yield insight into the competition between Ruderman-Kittel-Kasuya- Yosida interaction and Kondo interaction. We further find there exist scaling transformations, by applying which to the data with different hybridization strength, all the data collapses.
