Linear response theory of entanglement entropy

Linear response theory (LRT) is a powerful tool for investigating classical and quantum systems when perturbed by some external forces, connecting experimental observables with the correlation functions of the system in equilibrium states. On the other hand, the entanglement entropy (EE), or von Neumann entropy, is an important measure of non-classical correlations in quantum information science. As the EE is not a normal physical observable, developing a LRT for EE is valuable for understanding the changes of entanglement under an external perturbation. In this work, we present a framework of LRT of the von Neumann entropy. We found that for any composite quantum state the linear response of the von Neumann entanglement entropy can be quantified by a special correlation function. Consequently, we can derive the corresponding Kubo formula and the susceptibility of the EE, which have the same properties as its conventional counterpart. We further found that the linear response of the EE is zero for maximally entangled or separable states, a unique feature of entanglement dynamics. A numerical verification of our analytical results is also given based on the XX spin chain model. Overall, the LRT of EE provides a useful tool in investigating and understanding EE.