Linear Response Theory of Entanglement Entropy

TL;DR

This paper develops a linear response theory for entanglement entropy in open quantum systems, linking it to observable responses, and reveals unique features of entanglement dynamics with numerical verification.

Contribution

It introduces the linear response framework for von Neumann entropy, defining Kubo formulas and susceptibility for EE, and uncovers its zero response for maximally entangled or separable states.

Findings

Linear response of EE is determined by observable response.

EE response is zero for maximally entangled or separable states.

Numerical verification using XX spin chain model confirms analytical results.

Abstract

Linear response theory (LRT) is a key tool in investigating the quantum matter, for quantum systems perturbed by a weak probe, it connects the dynamics of experimental observable with the correlation function of unprobed equilibrium states. Entanglement entropy(EE) is a measure of quantum entanglement, it is a very important quantity of quantum physics and quantum information science. While EE is not an observable, developing the LRT of it is an interesting thing. In this work, we develop the LRT of von Neumann entropy for an open quantum system. Moreover, we found that the linear response of von Neumann entanglement entropy is determined by the linear response of an observable. Using this observable, we define the Kubo formula and susceptibility of EE, which have the same properties of its conventional counterpart. Through using the LRT of EE, we further found that the linear response of EE will be zero for maximally entangled or separable states, this is a unique feature of entanglement dynamics. A numerical verification of our analytical derivation is also given using XX spin chain model. The LRT of EE provides a useful tool in investigating and understanding EE.