title: Tensor representation techniques for full configuration interaction: A Fock space approach using the canonical product format.
abstract: In this proof-of-principle study, we apply tensor decomposition techniques to the Full Configuration Interaction (FCI) wavefunction in order to approximate the wavefunction parameters efficiently and to reduce the overall computational effort. For this purpose, the wavefunction ansatz is formulated in an occupation number vector representation that ensures antisymmetry. If the canonical product format tensor decomposition is then applied, the Hamiltonian and the wavefunction can be cast into a multilinear product form. As a consequence, the number of wavefunction parameters does not scale to the power of the number of particles (or orbitals) but depends on the rank of the approximation and linearly on the number of particles. The degree of approximation can be controlled by a single threshold for the rank reduction procedure required in the algorithm. We demonstrate that using this approximation, the FCI Hamiltonian matrix can be stored with N(5) scaling. The error of the approximation that is introduced is below Millihartree for a threshold of ϵ = 10(-4) and no convergence problems are observed solving the FCI equations iteratively in the new format. While promising conceptually, all effort of the algorithm is shifted to the required rank reduction procedure after the contraction of the Hamiltonian with the coefficient tensor. At the current state, this crucial step is the bottleneck of our approach and even for an optimistic estimate, the algorithm scales beyond N(10) and future work has to be directed towards reduction-free algorithms.
authors.affiliation: Max-Planck-Institut for Chemical Energy Conversion, Stiftstraße 34-36, D-45470 Mülheim an der Ruhr, Germany.
authors.forename: Karl-Heinz
authors.initials: KH
authors.lastname: Böhm
authors.affiliation: Max-Planck-Institut for Chemical Energy Conversion, Stiftstraße 34-36, D-45470 Mülheim an der Ruhr, Germany.
authors.forename: Alexander A
authors.initials: AA
authors.lastname: Auer
authors.affiliation: Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Pontdriesch 14-16, D-52062 Aachen, Germany.
authors.forename: Mike
authors.initials: M
authors.lastname: Espig