  We analyse time evolution of spread complexity (SC) in an isolated
interacting quantum many-body system when it is subjected to a sudden quench.
The differences in characteristics of the time evolution of the SC for
different time scales is analysed, both in integrable and chaotic models. For a
short time after the quench, the SC shows universal quadratic growth,
irrespective of the initial state or the nature of the Hamiltonian, with the
time scale of this growth being determined by the local density of states. The
characteristics of the SC in the next phase depend upon the nature of the
system, and we show that depending upon whether the survival probability of an
initial state is Gaussian or exponential, the SC can continue to grow
quadratically, or it can show linear growth. To understand the behaviour of the
SC at late times, we consider sudden quenches in two models, a full random
matrix in the Gaussian orthogonal ensemble, and a spin-1/2 system with
disorder. We observe that for the full random matrix model and the chaotic
phase of the spin-1/2 system, the complexity shows linear growth at early times
and saturation at late times. The full random matrix case shows a peak in the
intermediate time region, whereas this feature is less prominent in the
spin-1/2 system, as we explain.
