Markovian entanglement dynamics under locally scrambled quantum evolution

We study the time evolution of quantum entanglement for a specific class of quantum dynamics, namely, the locally scrambled quantum dynamics, where each step of the unitary evolution is drawn from a random ensemble that is invariant under local (on-site) basis transformations. In this case, the average entanglement entropy follows a Markovian dynamics, such that the entanglement property of the future state can be inferred from the entanglement property of the unitary operator of the underlying quantum dynamics. We introduce the entanglement feature formulation to concisely organize the entanglement entropies over all subsystems into a many-body wave function, which allows us to describe the entanglement dynamics using an imaginary-time Schrodinger equation, such that various tools developed in quantum many-body physics can be applied. The framework enables us to investigate a variety of random quantum dynamics beyond Haar random circuits and Brownian circuits. We perform numerical simulations for these models and demonstrate the validity and prediction power of the entanglement feature approach.