Purification of correlated reduced density matrices

The notion of purification is generalized to treat correlated reduced density matrices. Traditionally, purification denotes the process by which a one-particle reduced density matrix (1-RDM) is made idempotent, that is. its eigenvalues are mapped to either 0 or 1. Purification of correlated RDMs is defined as the iterative process by which an arbitrary RDM is forced to, several necessary N-representability conditions. Using the unitary decomposition of RDMs and the positivity conditions, we develop an algorithm to purify the 2-RDM. The algorithm is applied within the solution of the contracted Schrodinger equation CSE for the 2-RDM [D. A. Mazziotti. Phys. Rev. A 57, 4219 (1998)]. Previous attempts to solve the CSE by powerlike methods have frequently produced divergent energies, but e show that the purification process, eliminates the divergent behavior for systematic and reliable convergence of the contracted power method to the N-particle energy.