Magnetic and singlet phases in the three-dimensional periodic Anderson Model

Heavy fermion materials are compounds in which localized $f$-orbitals hybridize with delocalized $d$ ones, leading to quasiparticles with large renormalized masses. The presence of strongly correlated $f$-electrons at the Fermi level may also lead to long-range order, such as magnetism, or unconventional superconductivity. From a theoretical point of view, the ``standard model'' for heavy fermion compounds is the Periodic Anderson Model (PAM). Despite being extensively scrutinized, its thermodynamic properties in three-dimensional lattices have not been carefully addressed by unbiased methodologies. Here we investigate the 3D PAM employing state-of-the-art finite temperature auxiliary field quantum Monte Carlo simulations. We present the behavior of the kinetic energy, the entropy, the specific heat, and the double occupancy as functions of the temperature and the hybridization strength. From these quantities, and by the analysis of the spin-spin correlation functions, we investigate the occurrence of magnetic phase transitions at finite temperatures, and determine the phase diagram of the model, including the behavior of the N\'eel temperature as a function of the external parameters.