Multiregion entanglement in locally scrambled quantum dynamics

We study the evolution of multi-region bipartite entanglement entropy under locally scrambled quantum dynamics and show that it can significantly modify the growth of single-region entanglement. We developed a novel theoretical framework, called the entanglement feature formalism, to organize all the multi-region entanglement systematically as a sign-free many-body state. We further propose a two-parameter matrix product state (MPS) ansatz to efficiently capture the exponentially many multi-region entanglement features. Using these tools, we are able to study the dynamics of the full entanglement spectrum and represent the evolution in the MPS parameter space. By comparing the dynamical constraints on the motion of entanglement cuts, we are able to identify different quantum dynamics models in a unifying entanglement feature Hamiltonian and calculate quantities such as the operator-averaged out-of-time-order correlator, butterfly and entanglement velocities. We find that multi-region effects only vanish for Haar random circuits. These developments could enable more efficient numerical simulations and more systematic theoretical understandings of the multi-region entanglement dynamics in quantum many-body systems.