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 $1+1\mathrm{D}$ 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 ${S}_{A}\ensuremath{\sim}ln(t)$, results from $\ensuremath{\sim}\sqrt{ln(t)}$ significant charge sectors, each of which contributes $\ensuremath{\sim}\sqrt{ln(t)}$ to the entropy. We compare our calculations 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.