1202.4907 (Michael Potthoff)

Static and dynamic variational principles for strongly correlated
electron systems    [PDF]

Michael Potthoff

The equilibrium state of a system consisting of a large number of strongly
interacting electrons can be characterized by its density operator. This gives
a direct access to the ground-state energy or, at finite temperatures, to the
free energy of the system as well as to other static physical quantities.
Elementary excitations of the system, on the other hand, are described within
the language of Green's functions, i.e. time- or frequency-dependent dynamic
quantities which give a direct access to the linear response of the system
subjected to a weak time-dependent external perturbation. A typical example is
angle-revolved photoemission spectroscopy which is linked to the
single-electron Green's function. Since usually both, the static as well as the
dynamic physical quantities, cannot be obtained exactly for lattice fermion
models like the Hubbard model, one has to resort to approximations. Opposed to
more ad hoc treatments, variational principles promise to provide consistent
and controlled approximations. Here, the Ritz principle and a generalized
version of the Ritz principle at finite temperatures for the static case on the
one hand and a dynamical variational principle for the single-electron Green's
function or the self-energy on the other hand are introduced, discussed in
detail and compared to each other to show up conceptual similarities and
differences. In particular, the construction recipe for non-perturbative
dynamic approximations is taken over from the construction of static mean-field
theory based on the generalized Ritz principle. Within the two different
frameworks, it is shown which types of approximations are accessible, and their
respective weaknesses and strengths are worked out. Static Hartree-Fock theory
as well as dynamical mean-field theory are found as the prototypical
approximations.

View original: http://arxiv.org/abs/1202.4907