Preliminary Assessment of the First-Order Density Matrix in Quantum Monte Carlo from Density Matrix Theory

The trial wave function commonly used in the quantumMonte Carlomethod consists of the product of up-spin and down-spin Slater determinants,allowing accurate calculations of multielectronic properties, althoughit is not antisymmetric under the exchange of electrons with oppositespins. An alternative description that overcomes these limitationsusing the Nth-order density matrix was already presented.This study introduces two new strategies based on the Dirac-Fockdensity matrix for QMC that still fully preserve antisymmetry andelectron indistinguishability. Simulations are performed for the groundand excited states of He, Li, and Be showing that the present formulationand the conventional separation of spins are appropriate for a correctdescription of these systems, except for singlet excited states ofthe He and Be atoms, and that a part of the antisymmetry (antiparallelspins) can be neglected.

Automated summary

The commonly used trial wave function in quantum Monte Carlo method is not antisymmetric under the exchange of electrons with opposite spins, but an alternative description using the Nth-order density matrix has been presented. This study introduces two new strategies based on the Dirac-Fock density matrix for QMC that fully preserve the antisymmetry and electron indistinguishability. Simulations for He, Li, and Be atoms show that the present formulation and the conventional separation of spins are appropriate except for singlet excited states of He and Be atoms, and that a part of the antisymmetry can be neglected.