Entanglement transport and thermalization in an isolated quantum spin chain

Entanglement transport is considered to be essential for understanding thermalization in an isolated quantum system. In this work, we study transport of entanglement entropy (EE) in the Ising model with the next-nearest-neighbor interaction as well as the transverse and longitudinal magnetic fields. We calculate EE in a spin chain which consists of a single spin at the edge (A) and the bulk part (B). We compare time-evolution of EE for two different initial settings: the one with entanglement between A and B and the other one without it. The propagation speed of EE can be estimated by the time at which the EEs starting from the two initial conditions show deviation. We find that EE propagates ballistically with a constant velocity and that the propagation speed is enhanced when thermalization occurs. We also calculate the propagation speed of EE from mutual information between A and a subsystem in B. The velocities calculated by the two different methods agree well. We will discuss the relation between propagation of EE and thermalization.