Expectation value constraints for the N-representability problem

It has long been known that reduced density matrices (RDM) can be used to obtain the exact ground state energy of many-particle Hamiltonians by performing a constrained minimization over the set of all N-representable reduced density matrices. In this paper, we present a set of N-representability constraints for both bosons and fermions based on expectation values. These expectation value constraints are derived from a simple yet nontrivial recursive formula, and can easily be included in RDM-based variational schemes. The expectation value constraints are shown to provide additional N-representability information when compared to existing N-representability constraints.