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IGPM444.pdf February 2016 
TITLE 
Tensor Representation Techniques for Full Configuration Interaction: A Fock Space Approach Using the Canonical Product Format 
AUTHORS 
KarlHeinz Böhm , Mike Espig, Alexander A. Auer 
ABSTRACT 
In this proofofprinciple study we apply tensor decomposition techniques to the Full Configuration Interaction (FCI) wavefunction in order to reduce the exponential scaling of the number of wavefunction parameters and
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 demon
strate that using this approximation, the FCI Hamiltonian matrix and the wavefunction parameters can be stored
with N5 scaling and the FCI problem can be solved with subexponential effort. 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 steps scales beyond N10 .

KEYWORDS 

CORRESPONDING AUTHOR 
Alexander A. Auer, Email: alexander.auer@cec.mpg.de 