An electronic quantity, the correlation strength, is defined as a necessary step for understanding the properties and trends in strongly correlated electronic materials. As a test case, this is applied to the different phases of elemental Pu. Within
the GW approximation we have surprisingly found a universal scaling relationship, where the f-electron bandwidth reduction due to correlation effects is shown to depend only on the local density approximation bandwidth and is otherwise independent of crystal structure and lattice constant.
The last decade has seen a large increase in the number of electronic-structure calculations that involve adding a Hubbard term to the local density approximation band-structure Hamiltonian. The Hubbard term is then solved either at the mean-field le
vel or with sophisticated many-body techniques such as dynamical mean field theory. We review the physics underlying these approaches and discuss their strengths and weaknesses in terms of the larger issues of electronic structure that they involve. In particular, we argue that the common assumptions made to justify such calculations are inconsistent with what the calculations actually do. Although many of these calculations are often treated as essentially first-principles calculations, in fact, we argue that they should be viewed from an entirely different point of view, viz., as phenomenological many-body corrections to band-structure theory. Alternatively, they may also be considered to be just a more complex Hubbard model than the simple one- or few-band models traditionally used in many-body theories of solids.
