Spread complexity evolution in quenched interacting quantum systems

We analyze time evolution of spread complexity (SC) in an isolated interacting quantum many-body system when it is subjected to a sudden quench. Characteristics features of the time evolution of the SC after the quench are analyzed for different timescales, 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 timescale of this growth being determined by the local density of states. The characteristics of the SC in the next phase depend on the nature of the system, and we show that, depending on 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 behavior 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 SC 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.