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

Spread complexity evolution in quenched interacting quantum systems