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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.