Optimal multiconfiguration approximation of an N -fermion wave function

We propose a simple iterative algorithm to construct the optimal multiconfiguration approximation of an $N$-fermion wave function. Namely, $M\ensuremath{\ge}N$ single-particle orbitals are sought iteratively so that the projection of the given wave function in the ${C}_{M}^{N}$-dimensional configuration subspace is maximized. The algorithm has a monotonic convergence property and can be easily parallelized. The significance of the algorithm on the study of geometric entanglement in a multifermion system and its implication on the multiconfiguration time-dependent Hartree-Fock (MCTDHF) are discussed. The ground state and real-time dynamics of spinless fermions with nearest-neighbor interaction are studied using this algorithm, discussing several subtleties.