Shannon Information Entropy in Position Space for Two-Electron Atomic Systems

Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited states in helium-like systems. In this work, we adopt another entropic measure, Shannon entropy, to probe the nature of correlation effects. Besides the results of the Shannon entropy in coordinate space for the singlet ground states of helium-like systems including positronium negative ion, hydrogen negative ion, helium atom, and lithium positive ion, we also show results for systems with nucleus charge around the ionization threshold.

Quantification of Entanglement Entropies for Doubly Excited States in Helium

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.

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

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.

Quantification of linear entropy for quantum entanglement in He, H- and Ps- ions using highly-correlated Hylleraas functions

The quantum entanglement for the two electrons in three-body atomic systems such as the helium atom, the hydrogen negative ion and the positronium negative ion are investigated by employing highly correlated Hylleraas functions to represent the ground states of such systems. As a measure of the spatial entanglement, the linear entropy of the reduced density matrix is calculated for the ground states. The required four-electron (12-dimensional) integrals are solved analytically such that they are suitable for machine computations. Results are compared with other calculations when available.