The cumulant two-particle reduced density matrix as a measure of electron correlation and entanglement

摘要

Several measures of electron correlation are compared based on two criteria:(i) the presence of a unique mapping between the reduced variables in the measure and the many-electron wave function and (ii) the linear scaling of the measure and its variables with system size.We propose the squared Frobenius norm of the cumulant part of the two-particle reduced density matrix (2-RDM) as a measure of electron correlation that satisfies these criteria.An advantage of this cumulant-based norm is its ability to measure the correlation from spin entanglement,which is not contained in the correlation energy.Alternative measures based on the 2-RDM,such as the von Neumann entropy,do not scale linearly with system size.Properties of the measures are demonstrated with Be,F_2,HF,N_2,and a hydrogen chain.