Efficient simulations of Hartree-Fock equations by an accelerated gradient descent method

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Simulating many-particle quantum systems is computationally intensive.
• Hartree-Fock equations are fundamental for understanding electron interactions.
• Efficient numerical methods are crucial for advancing quantum simulations.

Purpose of the Study:

• To develop convergence acceleration procedures for gradient descent methods.
• To enhance the efficiency of simulating Hartree-Fock equations for many-particle systems.
• To improve computational methods for quantum mechanical problems.

Main Methods:

• Optimization of preconditioning operator parameters.
• Single-mode elimination technique adapted for many-particle systems.
• Novel extension for simultaneous multiple-mode elimination.

Main Results:

• Acceleration of gradient descent by at least two orders of magnitude.
• Demonstrated performance on a two-dimensional helium-on-graphene model.
• Single- and multiple-mode elimination outperform Anderson Acceleration.

Conclusions:

• Developed efficient acceleration techniques for Hartree-Fock simulations.
• The methods significantly improve convergence rates for many-particle problems.
• Proposed techniques are applicable to other iterative methods for interacting particles.