Volume-Collapse Transitions in the Rare Earth Metals

We describe current experimental and theoretical understanding of the pressure-induced volume collapse transitions occurring in the early trivalent rare earth metals. General features of orbitally realistic mean-field based theories used to calculate these transitions are discussed. Potential deficiencies of these methods are assessed by comparing mean field and exact Quantum Monte Carlo solutions for the one-band Hubbard and two-band periodic Anderson lattice models. Relevant parameter regimes for these models are determined from local density constrained occupation calculations.