Active-space N-representability constraints for variational two-particle reduced density matrix calculations

Area of Science:

• Quantum chemistry
• Computational physics
• Many-body theory

Background:

• Calculating the ground-state energy of fermionic systems is crucial in many areas of science.
• Traditional methods often rely on approximations or computationally expensive techniques.
• The two-particle reduced density matrix (2-RDM) offers a more direct route if accurate N-representability conditions are available.

Purpose of the Study:

• To introduce a novel class of linear N-representability conditions for the 2-RDM.
• To improve the accuracy of ground-state energy calculations for fermionic systems.
• To demonstrate the effectiveness of these conditions on a relevant model system.

Main Methods:

• Developed a new set of linear N-representability conditions based on exact calculations within a reduced active space.
• Utilized the 2-RDM methodology, which allows for the combination of information from different active spaces.
• Incorporated active-space constraints to iteratively refine the ground-state energy estimate.

Main Results:

• The new N-representability conditions significantly improve upon traditional 2-positivity constraints.
• The methodology was successfully applied to the 1D Hubbard model, yielding more accurate ground-state energies.
• The computational scaling remained comparable to existing methods, offering a practical advantage.

Conclusions:

• The introduced linear N-representability conditions provide a powerful tool for accurate ground-state energy calculations.
• Combining information from various active spaces via the 2-RDM methodology enhances computational efficiency and accuracy.
• This approach represents a significant advancement for studying complex fermionic systems.