  We discuss the general formalism and validity of weak-coupling perturbation
theory as an impurity solver for nonequilibrium dynamical mean-field theory.
The method is implemented and tested in the Hubbard model, using expansions up
to fourth order for the paramagnetic phase at half filling and third order for
the antiferromagnetic and paramagnetic phase away from half filling. We explore
various types of weak-coupling expansions and examine the accuracy and
applicability of the methods for equilibrium and nonequilibrium problems. We
find that in most cases an expansion of local self-energy diagrams including
all the tadpole diagrams with respect to the Weiss Green's function
(bare-diagram expansion) gives more accurate results than other schemes such as
self-consistent perturbation theory using the fully interacting Green's
function (bold-diagram expansion). In the paramagnetic phase at half filling,
the fourth-order bare expansion improves the result of the second-order
expansion in the weak-coupling regime, while both expansions suddenly fail at
some intermediate interaction strength. The higher-order bare perturbation is
especially advantageous in the antiferromagnetic phase near half filling. We
use the third-order bare perturbation expansion within the nonequilibrium
dynamical mean-field theory to study dynamical symmetry breaking from the
paramagnetic to the antiferromagnetic phase induced by an interaction ramp in
the Hubbard model. The results show that the order parameter, after an initial
exponential growth, exhibits an amplitude oscillation around a nonthermal value
followed by a slow drift toward the thermal value. The transient dynamics seems
to be governed by a nonthermal critical point, associated with a nonthermal
universality class, which is distinct from the conventional Ginzburg-Landau
theory.
