Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Quantum Monte Carlo (QMC) methods are crucial for simulating complex quantum systems.
• Fermionic systems with periodic boundary conditions (PBC) often face challenges in achieving efficient convergence.
• The thermodynamic limit represents the macroscopic behavior of a system.

Purpose of the Study:

• To develop and test Quantum Monte Carlo algorithms incorporating wave function phase twists.
• To investigate the impact of twist averaging on the convergence rate for fermionic systems.
• To analyze the computational efficiency and applicability of twist averaging in various models.

Main Methods:

• Development of QMC algorithms utilizing a "twist" or phase in the wave function.
• Application of twist averaging to systems with periodic boundary conditions.
• Determination of convergence exponents for energy components in Coulomb systems.
• Testing on free particles, Stoner model, and electron gas using various wave functions (Hartree-Fock, Slater-Jastrow, three-body, backflow).

Main Results:

• Twist averaging accelerates convergence to the thermodynamic limit for metallic systems compared to standard PBC.
• This acceleration is particularly effective for properties involving kinetic energy.
• The computational complexity remains the same as standard PBC.
• Convergence exponents for energy components were determined for Coulomb systems.

Conclusions:

• Twist averaging is an efficient technique for improving QMC simulations of fermionic systems.
• The method offers faster convergence without increasing computational cost.
• It is applicable to various models and wave function types, including those in the grand canonical ensemble.