  In this work we formulate the nonequilibrium dynamical renormalization group
(ndRG). The ndRG represents a general renormalization-group scheme for the
analytical description of the real-time dynamics of complex quantum many-body
systems. In particular, the ndRG incorporates time as an additional scale which
turns out to be important for the description of the long-time dynamics. It can
be applied to both translational invariant and disordered systems. As a
concrete application we study the real-time dynamics after a quench between two
quantum critical points of different universality classes. We achieve this by
switching on weak disorder in a one-dimensional transverse-field Ising model
initially prepared at its clean quantum critical point. By comparing to
numerically exact simulations for large systems we show that the ndRG is
capable of analytically capturing the full crossover from weak to infinite
randomness. We analytically study signatures of localization in both real space
and Fock space.
