Evolution of Entanglement in Holographic Systems

Javier Abajo-Arrastia, João Aparício, Esperanza López

I. Ya. Aref’eva, I. V. Volovich, O. V. Inozemcev

We consider entanglement entropy quantities for a three-part system, namely, the tripartite information, total correlation, and so-called secrecy monotone. A holographic approach is used to calculate the time evolution of the entanglement entropy during nonequilibrium heating, which leads to holographic definitions of these quantities. We study time dependence of these three quantities.

Weibo Mao, Masahiro Nozaki A

A bstract In this paper, we investigate the entanglement dynamics induced by a composite operator, defined as the local operator evolved with the time evolution operator constructed out of the Euclidean and Lorentzian ones. The systems under consideration are described by two-dimensional holographic conformal field theories (2d holographic CFTs), the theories described by gravity. Then, we find that the time ordering of Euclidean and Lorentzian time evolutions determines whether the time evolution, inducing the operator growth, is unitary. We also establish the relation between entanglement entropy and energy densities. This relation provides the entanglement entropy as a function of those densities. By exploiting this relation, we find that the time ordering, i.e., whether the time evolution is unitary, determines the late-time behavior of bipartite entanglement and non-local correlation. We also investigate how the decay of the quasiparticle influences the bipartite entanglement and non-local correlation. Furthermore, we investigate the gravity dual of the systems considered in this paper.

Shinsei Ryu, Tadashi Takayanagi

悠輝 中口

I. Ya. Aref’ eva, Igor Vasil'evich Volovich, Oleg Valerievich Inozemcev

We analyze how the compositeness of a system affects the characteristic time of equilibration. We study the dynamics of open composite quantum systems strongly coupled to the environment after a quantum perturbation accompanied by nonequilibrium heating. We use a holographic description of the evolution of entanglement entropy. The nonsmooth character of the evolution with holographic entanglement is a general feature of composite systems, which demonstrate a dynamical change of topology in the bulk space and a jumplike velocity change of entanglement entropy propagation. Moreover, the number of jumps depends on the system configuration and especially on the number of composite parts. The evolution of the mutual information of two composite systems inherits these jumps. We present a detailed study of the mutual information for two subsystems with one of them being bipartite. We find five qualitatively different types of behavior of the mutual information dynamics and indicate the corresponding regions of the system parameters.