Recovery of Mutual Information by Inhomogeneous Quenches in Two-dimensional Conformal Field Theories

Abstract

We study the dynamics of mutual information during the evolution induced by the M ̈obius/sine-squared deformed Hamiltonians (M ̈obius/SS deformed Hamiltonians) in two-dimensional conformal field theories (2d CFTs), starting from the thermofield double state, the state on the double Hilbert spaces. Under the SSD time-evolution, the time-dependence of mutual information shows the Bell pairs, initially shared by the subsystems of these double Hilbert spaces, may revive even after the mutual information for the small subsystems is completely destroyed. This mutual information is robust against the strong scrambling dynamics. As a consequence, the steady state has the non-local correlation shared by three parties but does not have the one shared by the two parties. From the gravity side, the wormhole may non-linearly grow with time during the evolution considered in this project. We also propose effective pictures that describe the dynamics of mutual information. We plan to present the results of this project.