Dynamics of Charge-Resolved Entanglement after a Local Quench

Abstract: Quantum entanglement and its main quantitative measures, the entanglement entropy and entanglement negativity, play a central role in many body physics. An interesting twist arises when the system considered has symmetries leading to conserved quantities: Recent studies introduced a way to define, represent in field theory, calculate for 1+1D conformal systems, and measure, the contribution of individual charge sectors to the entanglement measures between different parts of a system in its ground state. In this paper, we apply these ideas to the time evolution of the charge-resolved contributions to the entanglement entropy and negativity after a local quantum quench. We employ conformal field theory techniques and find that the known dependence of the total entanglement on time after a quench, $S_A \sim \log(t)$, results from $\sim\sqrt{\log(t)}$ significant charge sectors, each of which contributes $\sim\sqrt{\log(t)}$ to the entropy. We compare our calculation to numerical results obtained by the time-dependent density matrix renormalization group algorithm and exact solution in the noninteracting limit, finding good agreement between all these methods.