Evolution of single-site entanglement in a non-equilibrium 1D critical Ising chain

Non-equilibrium time evolution of entanglement is considered in a 1D critical Ising chain. At the point of the quantum phase transition, this system is maximally entangled in its thermal ground state. Using the scaling analytical expressions for the magnetization profile, the behavior of the non-equilibrium analog is studied for the single-site entanglement entropy. The latter quantity becomes the usual von Neuman entropy during the system evolution. We choose the initial finite domain configuration, which gives quite general picture of evolution processes. However the obtained results can be generalized to more complicated initial configurations, as well as to the anisotropic XY chain. It is shown that the relaxation time of single-site entanglement is strongly dependent on the characteristic size of inhomogeneity of the input state. This is an important issue for possible realization of a rescalable solid-state quantum computer.