Efficient evaluation of AGP reduced density matrices.

Area of Science:

• Quantum chemistry
• Computational physics
• Many-body theory

Background:

• Calculating properties of quantum systems often requires expensive computations.
• Reduced density matrices (RDMs) are crucial for understanding electronic structure.
• Existing methods for RDMs can be computationally prohibitive for large systems.

Purpose of the Study:

• To develop an efficient algorithm for calculating RDMs.
• To enable the study of larger and more complex quantum systems.
• To reduce the computational cost associated with RDM calculations.

Main Methods:

• An algorithm is proposed and implemented to calculate the norm and RDMs.
• The method applies to the antisymmetrized geminal power of any rank.
• The algorithm exhibits polynomial scaling with a quadratic cost per RDM element.

Main Results:

• The algorithm is demonstrated to be very fast through numerical tests.
• The method reliably treats systems with thousands of orbitals and hundreds of electrons.
• Reconstruction formulas are presented to decompose higher-order RDMs, further reducing cost.

Conclusions:

• The proposed algorithm offers a significant advancement in calculating RDMs.
• This method opens possibilities for studying larger quantum systems efficiently.
• The computational cost reduction makes complex electronic structure calculations more feasible.