Diffusion monte carlo methods with a fixed number of walkers

Area of Science:

• Computational Physics
• Quantum Mechanics
• Stochastic Methods

Background:

• Diffusion Monte Carlo (DMC) is a powerful quantum mechanical simulation technique.
• Pure Diffusion Monte Carlo (PDMC) methods, a variant without branching, face challenges with divergence.
• Accurate simulations of quantum systems require robust and unbiased computational approaches.

Purpose of the Study:

• To rigorously prove the divergence of pure diffusion Monte Carlo (PDMC) methods.
• To introduce a novel, bias-free Monte Carlo method.
• To demonstrate the applicability of the new method through calculations on a model quantum system.

Main Methods:

• Mathematical proof of divergence for PDMC methods.
• Development of a hybrid Monte Carlo approach combining DMC and PDMC.
• Minimal stochastic reconfiguration of the walker population.
• Application to a system of coupled quantum rotators.

Main Results:

• A rigorous proof demonstrates the divergence of pure diffusion Monte Carlo (PDMC) methods.
• A new bias-free Monte Carlo method is presented, integrating DMC and PDMC.
• Illustrative calculations on coupled quantum rotators showcase the method's utility.

Conclusions:

• Pure diffusion Monte Carlo (PDMC) methods are inherently divergent.
• The proposed bias-free Monte Carlo method offers a viable alternative for quantum simulations.
• The new method shows promise for accurate calculations in complex quantum systems.