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

TL;DR

This paper investigates the challenges of calculating entanglement entropy in quantum transport models using Kadanoff-Baym equations, highlighting issues with approximate self-energies and identifying the T-matrix approximation as a reliable scheme.

Contribution

The study demonstrates that certain approximate self-energies can yield negative double occupancy, and shows that the T-matrix approximation reliably remains non-negative, providing analytical proof.

Findings

Double occupancy can become negative with some approximations.

T-matrix approximation remains non-negative and matches exact results at low density.

Entanglement transmission is reduced by interactions but enhanced by current flow.

Abstract

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 $< \hat{n}_{R \uparrow} \hat{n}_{R \downarrow} >$, 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 $< \hat{n}_{R \uparrow} \hat{n}_{R \downarrow} >$ 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 $< \hat{n}_{R \uparrow} \hat{n}_{R \downarrow} >$. 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.