Tensor representation techniques for full configuration interaction: A Fock space approach using the canonical...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Full Configuration Interaction (FCI) calculations are computationally expensive due to the exponential scaling of wavefunction parameters.
• Developing efficient methods to approximate FCI wavefunctions is crucial for advancing quantum chemistry simulations.

Purpose of the Study:

• To apply tensor decomposition techniques to FCI wavefunctions for efficient parameter approximation.
• To reduce the computational effort required for FCI calculations.

Main Methods:

• Formulating the wavefunction ansatz in an occupation number vector representation to ensure antisymmetry.
• Applying canonical product format tensor decomposition to represent the Hamiltonian and wavefunction in a multilinear product form.
• Utilizing a rank reduction procedure controlled by a single threshold for approximation.

Main Results:

• The number of wavefunction parameters scales linearly with the number of particles, not exponentially.
• The FCI Hamiltonian matrix can be stored with N(5) scaling.
• Approximation errors are below Millihartree for a threshold of ϵ = 10(-4) without convergence issues.

Conclusions:

• Tensor decomposition offers a promising conceptual approach to reduce computational cost in FCI calculations.
• The rank reduction procedure is currently a bottleneck, scaling beyond N(10).
• Future research should focus on developing reduction-free algorithms for this method.