Quantification of entanglement entropy in helium by the Schmidt-Slater decomposition method

TL;DR

This paper investigates the spatial entanglement entropy in helium atoms using highly correlated wave functions and the Schmidt-Slater decomposition method to accurately compute entanglement measures.

Contribution

It introduces the application of the Schmidt-Slater decomposition to helium's two-electron wave functions for precise entanglement quantification.

Findings

Calculated von Neumann and linear entropies for various helium states.

Demonstrated the effectiveness of the Schmidt-Slater method in entanglement analysis.

Provided detailed eigenvalues of the reduced density matrix for helium states.

Abstract

In this work, we present an investigation on the spatial entanglement entropies in the helium atom by using highly correlated Hylleraas functions to represent the S-wave states. Singlet-spin 1sns 1Se states (with n = 1 to 6) and triplet-spin 1sns 3Se states (with n = 2 to 6) are investigated. As a measure on the spatial entanglement, von Neumann entropy and linear entropy are calculated. Furthermore, we apply the Schmidt-Slater decomposition method on the two-electron wave functions, and obtain eigenvalues of the one-particle reduced density matrix, from which the linear entropy and von Neumann entropy can be determined.