Optimal multi-configuration approximation of an N-fermion wave function

Abstract

We propose a simple iterative algorithm to construct the optimal multi-configuration approximation of an $N$-fermion wave function. That is, $M\ge N$ 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 entanglement in a multi-fermion system and its implication on the multi-configuration time-dependent Hartree-Fock (MCTDHF) are discussed. The ground state and real-time dynamics of spinless fermions with nearest-neighbor interactions are studied using this algorithm, discussing several subtleties.

12 pages, 7 figures. Any comment is welcome and appreciated

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• Many-body localization in the Fock space of natural orbitals
• Quantifying the effect of interactions in quantum many-body systems
• Optimal Slater-determinant approximation of fermionic wave functions
• Lecture Notes: many-body quantum dynamics with MCTDH-X
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• Orbital and electronic entanglement in quantum teleportation schemes
• Geometric entanglement in the Laughlin wave function
• Fock-space geometry and strong correlations in many-body localized systems