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Bulletin of the American Physical Society

Calculations of Entanglement Entropy in Two-Electron Atomic Systems Using Highly-Correlated Hylleraas Functions

Y. K. Ho, Chien-Hao Lin, Y.-C. Lin

Published Jun 4, 2013• 0 citations
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In this work, we study the quantum entanglement for doubly excited resonance states in two-electron atomic systems such as the H - and Ps - ions and the He atom by using highly correlated Hylleraas type functions The resonance states are determined by calculation of density of resonance states with the stabilization method. The spatial (electron-electron orbital) entanglement entropies (linear and von Neumann) for the low-lying doubly excited states are quantified using the Schmidt-Slater decomposition method.
In the present work, we report an investigation on quantum entanglement in the doubly excited 2s2 1Se resonance state of the positronium negative ion by using highly correlated Hylleraas type wave functions, determined by calculation of the density of resonance states with the stabilization method. Once the resonance wave function is obtained, the spatial (electron-electron orbital) entanglement entropies (von Neumann and linear) can be quantified using the Schmidt decomposition method. Furthermore, Shannon entropy in position space, a measure for localization (or delocalization) for such a doubly excited state, is also calculated.
Abstract Information entropies, such as Rényi, Fisher, and Shannon, are calculated for the 1s 2 -state of the two-electron series, in position space. It is considered that the exponential cosine screened Coulomb potential (ECSCP) describes the medium. Explicit correlated Hylleraas functions with 3-parameter are used to focus on getting the most distinctive physical features of the inter-electronic repulsion results. In one- and two-electron charge densities, the numerical values of the information entropies and their ratios are calculated. Fisher-Shannon, and Fisher-Rényi information products that measure the electron-electron correlation strength, are calculated and discussed. Also, we used the contour maps and 3D-graphs to visualize how the interplay between inter-electronic repulsion and electrons-nuclear charge interaction determines the variation of information entropies as a function of the nuclear charge and the screening parameter. In this work, an expression for the divergence in Hylleraas coordinates has been derived and the results of the information quantities for two-electron systems with ECSCP have been calculated, in one-and two-electron densities, for the first time.