Quantification of Entanglement Entropies for Doubly Excited States in Helium

TL;DR

This paper investigates quantum entanglement in doubly excited helium states using correlated wave functions and entropy measures, providing new insights into electron correlation in resonance states.

Contribution

It introduces a method to quantify entanglement in doubly excited helium states using Hylleraas functions and entropy measures, combining numerical and analytical approaches.

Findings

Entanglement measures for specific helium resonance states are calculated.

The linear and von Neumann entropies show consistent results.

The approach enhances understanding of electron correlation in excited states.

Abstract

In this work, we study the quantum entanglement for doubly excited resonance states in helium by using highly correlated Hylleraas type functions to represent such states of the two-electron system. The doubly-excited resonance states are determined by calculation of density of resonance states under the framework of the stabilization method. The spatial (electron-electron orbital) entanglement measures for the low-lying doubly excited 2s2, 2s3s, and 2p2 1Se states are carried out. Once a resonance state wave function is obtained, the linear entropy and von Neumann entropy for such a state are quantified using the Schmidt-Slater decomposition method. To check the consistence, linear entropy is also determined by solving analytically the needed four-electron (12-dimensional) integrals.