Can we always get the entanglement entropy from the Kadanoff-Baym equations? The case of the T-matrix approximation

We study the time-dependent transmission of entanglement entropy through an out-of-equilibrium model interacting device in a quantum transport set-up. The dynamics is performed via the Kadanoff-Baym equations within many-body perturbation theory. The double occupancy <(n) over cap (R dagger)(n) over cap (R down arrow)>, needed to determine the entanglement entropy, is obtained from the equations of motion of the single-particle Green's function. A remarkable result of our calculations is that <(n) over cap (R dagger)(n) over cap (R down arrow)> can become negative, thus not permitting to evaluate the entanglement entropy. This is a shortcoming of approximate, and yet conserving, many-body self-energies. Among the tested perturbation schemes, the T-matrix approximation stands out for two reasons: it compares well to exact results in the low-density regime and it always provides a non-negative <(n) over cap (R dagger)(n) over cap (R down arrow)> For the second part of this statement, we give an analytical proof. Finally, the transmission of entanglement across the device is diminished by interactions but can be amplified by a current flowing through the system. Copyright (C) EPLA, 2011