Symmetric tensor decomposition description of fermionic many-body wave functions

Area of Science:

• Quantum chemistry
• Computational physics
• Theoretical chemistry

Background:

• Configuration interaction (CI) is a fundamental quantum chemistry method for describing electron correlation in interacting fermions.
• The standard CI expansion can become computationally intractable due to its extremely long series, limiting its application to larger systems.
• Developing more efficient and practical methods to achieve the full CI limit is crucial for accurate molecular electronic structure calculations.

Purpose of the Study:

• To develop a numerically tractable and compact representation of the configuration interaction (CI) series.
• To introduce a novel approach for accelerating the convergence of CI expansions towards the full CI state.
• To enhance the practicability of achieving high-accuracy electronic structure calculations using variational methods.

Main Methods:

• Application of symmetric tensor decomposition to transform the conventional CI series.
• Reformulation of the CI series into a compact form starting with the Hartree-Fock state.
• Numerical validation using small molecular systems to assess convergence properties.

Main Results:

• The symmetric tensor decomposition method converts the long CI series into a compact and numerically manageable form.
• The converted CI series demonstrates rapid convergence to the full-CI state, as evidenced by numerical tests.
• The length of the new CI series shows moderate growth with increasing system complexity.

Conclusions:

• The symmetric tensor decomposition approach offers a practical and efficient alternative for achieving full CI accuracy.
• This method significantly enhances the tractability of wave function theory for interacting fermions.
• The new approach holds promise for advancing computational chemistry and materials science by enabling more accurate electronic structure predictions.