Ab initio study on fcc Pr with correlation matrix renormalization theory

We studied fcc praseodymium (Pr) with the ab initio correlation matrix renormalization theory (CMRT) explicitly calculating the Coulomb interactions among basis orbitals and without using any adjustable parameters to work for strongly correlated electron systems. We calculated its total energy in a paramagnetic ground state and studied the role of the correlated $4f$ electrons in the system. Good agreement was obtained between CMRT and experiments in the pressure volume dependence of the fcc phase. We also compared the CMRT results against other theoretical methods including local density $\text{approximation}+\text{dynamical}$ mean-field theory and showed consistent results among them. Moreover, we found the normalized local charge fluctuation of the $4f$ electrons as the function of volume exhibits a clear slope change at the volume collapse region, indicating a switch in their correlation nature there.