Entanglement Thermalization and Local Conservation Laws

We study the thermalization of entanglement entropy in one-dimensional spin chains under the unitary dynamics of a nonintegrable Hamiltonian or periodic driving by Floquet operators. Using full diagonalization of the Hamiltonian matrix and the Floquet operators, we analyze the time evolution of entanglement entropy starting from various initial conditions, including initial states with entanglement in excess of the thermal equilibrium value. It is found that the thermalization of entanglement entropy is coupled to local conservation laws when approaching equilibrium, and the absence of conservation laws in the Floquet system allows the entanglement entropy to thermalize more rapidly than it does in the corresponding Hamiltonian.