Quantification of entanglement entropies in two-electron atomic systems by the Schmidt-Slater decomposition method

We have carried out an investigation of the linear entropy and the von Neumann entropy for spatial (electron-electron orbital) entanglement for the two spin-1/2 fermions (electrons) in helium-like atomic systems. Hylleraas-type wave functions, in which the inter-electronic terms are included to take into account of correlation effects, are used to represent the ground and excited states of the two-electron wave functions with different nucleus charges. To quantify the entanglement entropies, we utilize the partial wave expansion procedure on the correlated Hylleraas functions, and employ the Schmidt-Slater decomposition method (see [1], and the references therein) to extract the eigenvalues for the one-particle reduced density matrix, from which the entropies can be determined. Our present results for linear entropy have shown good agreement with other available calculations using different methods [2, 3]. We will present our new results for the von Neumann entropy at the meeting.\\[4pt] [1] Ko\'{s}cik, P. \textit{Phys. Lett. A} \textbf{377}, 2393 (2013);\\[0pt] [2] Lin, Y.-C., Lin, C.-Y., and Ho, Y. K., \textit{Phys. Rev. A} \textbf{87}, 022316 (2013);\\[0pt] [3] Lin, C.-H., Lin, Y.-C. and Ho, Y. K., \textit{Few-Body Syst.} \textbf{54}, 2147 (2013).