  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 level 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.
