Approximate solution for electron correlation through the use of Schwinger probes

Quantum energies and two-particle reduced density matrices (2-rdms) may be determined without using the N-particle wavefunction by combining the reconstruction of higher rdms from lower rdms and the contracted Schrödinger equation. In this letter we derive a systematic procedure for obtaining reconstruction functionals through the use of Schwinger probes. Previous functionals for the 3 and 4-rdms are generated as well as new functionals for higher rdms. Through a quasi-spin model we demonstrate that the 5-rdm, normalized to unity, may be reconstructed from lower rdms with the accuracy of its elements ranging from 10−4 for five fermions to 10−8 for fifty fermions.