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

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.

6 pages, 6 figures

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Cited by in corpus (8)

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• Disorder and interactions in systems out of equilibrium: The exact independent-particle picture from density functional theory
• Transport of Correlated Electrons through Disordered Chains: A Perspective on Entanglement, Conductance, and Disorder Averaging
• Efficient computation of the second-Born self-energy using tensor-contraction operations
• Nonequilibrium Green's function approach to the pair distribution function of quantum many-body systems out of equilibrium