Variational occupation numbers to a M\"uller-type pair-density

TL;DR

This paper introduces a parametric one-matrix based on a point-wise decomposition of the pair-density, enabling the exact calculation of the ground-state energy in a correlated two-particle system through a M"uller-type partitioning.

Contribution

It presents a novel parametric one-matrix approach that achieves exact ground-state energies for a solvable two-particle model using a M"uller-type pair-density decomposition.

Findings

The method yields the exact ground-state energy for the model system.

The approach demonstrates robust performance in energy optimization.

It provides a new way to approximate pair-densities in correlated systems.

Abstract

Based on a parametric point-wise decomposition, a kind of isospectral deformation, of the exact one-particle probability density of an externally confined, analytically solvable interacting two-particle model system we introduce the associated parametric ($p$) one-matrix and apply it in the conventional M\"uller-type partitioning of the pair-density. Using the Schr\"odinger Hamiltonian of the correlated system, the corresponding approximate ground-state energy $E_p$ is then calculated. The optimization-search performed on $E_p$ with such restricted informations has a robust performance and results in the exact ($ex$) ground-state energy for the correlated model system $E_p=E_{ex}$.