Coexistence of Charge Order and Antiferromagnetic Order in an Extended Periodic Anderson Model

The competition between the RKKY interaction and the Kondo effect leads to a magnetic phase transition, which occurs ubiquitously in heavy fermion materials. However, there are more and more experimental evidences indicating that the valence fluctuation plays an essential role in the Ce- and Y-based compounds. We study an extended periodic Anderson model (EPAM) which includes the onsite Coulomb repulsion U_cf between the localized electrons and conduction electrons. By employing the density matrix embedding theory, we investigate the EPAM in the symmetric case at half filling. By fixing the onsite Coulomb repulsion U of the localized electrons to an intermediate value, the interplay between the RKKY interaction, the Kondo effect and the Coulomb repulsion U_cf brings rich physics. We find three different phases, the antiferromagnetic phase, the charge order phase and paramagnetic phase. When the hybridization strength V between the localized orbital and the conduction orbital is small, the Kondo effect is weak so that the AF phase and the CO phase are present. The phase transition between the two long-range ordered phase is of first order. We also find a coexistence region between the two phases. As V increases, the Kondo effect becomes stronger, and the paramagnetic phase appears between the other two phases.