  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.
