Quantum entanglement of helium-like systems with varying-Z: compact state-of-the-art CI wave functions

• Published in: Journal of physics. B, Atomic, molecular, and optical physics Vol. 48; no. 17; pp. 175002 - 9
• Main Authors: López-Rosa, S, Esquivel, R O, Plastino, A R, Dehesa, J S
• Format: Journal Article
• Language: English
• Published: IOP Publishing 14.09.2015
• Subjects: Benchmarking; Computational efficiency; Density; energy correlation versus entanglement; Entanglement; Entropy; linear entanglement entropy; Mathematical analysis; quantum entanglement of helium-like systems; Quantum mechanics; State of the art; von Neumann entanglement entropy; Wave functions
• ISSN: 0953-4075; 1361-6455
• DOI: 10.1088/0953-4075/48/17/175002

In this work we have performed state-of-the-art configuration-interaction (CI) calculations to determine the linear and von Neumann entanglement entropies for the helium-like systems with varying nuclear charge Z in the range . The focus of the work resides on determining accurate entanglement values for 2-electron systems with the lowest computational cost through compact CI-wave functions. Our entanglement results for the helium atom fully agree with the results obtained with higher quality wave functions of the Kinoshita type (Dehesa [5]). We find that the correlation energy is linearly related to the entanglement measures associated with the linear and von Neumann entropies of the single-particle reduced density matrizes, which sheds new light on the physical implications of entanglement in helium-like systems. Moreover, we report CI-wave-function-based benchmark results for the entanglement values for all members of the helium isoelectronic series with an accuracy similar to that of Kinoshita-type wave functions. Finally, we give parametric expressions of the linear and von Neumann entanglement measures for two-electron systems as Z varies from 1 to 10.