The lowest excited configuration of harmonium

TL;DR

This paper investigates the lowest excited (triplet) state of the harmonium model using phase space methods to explore the relationship between entanglement and correlation energy, extending prior ground state studies.

Contribution

It provides a comprehensive analysis of the excited state of harmonium and its entanglement properties, which were previously unexplored.

Findings

Characterizes the triplet excited state of harmonium

Analyzes entanglement measures in relation to correlation energy

Uses phase space Wigner quasiprobabilities for the study

Abstract

The harmonium model has long been regarded as an exactly solvable laboratory bench for quantum chemistry [Heisenberg, 1926]. For studying correlation energy, only the ground state of the system has received consideration heretofore. This is a spin singlet state. In this work we exhaustively study the lowest excited (spin triplet) harmonium state, with the main purpose of revisiting the relation between entanglement measures and correlation energy for this quite different species. The task is made easier by working with Wigner quasiprobabilities on phase space.