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Published on: September 5, 2019
Population size bias in descendant-weighted diffusion quantum Monte Carlo simulations
1Department of Chemistry, University of Tennessee, Knoxville, 37996, USA.
Summary
Population size is critical for accurate diffusion quantum Monte Carlo (DQMC) simulations. Insufficient population sizes lead to significant biases in expectation values, especially in higher dimensions.
Area of Science:
- Quantum mechanics
- Computational physics
- Statistical mechanics
Background:
- Diffusion Quantum Monte Carlo (DQMC) simulations are used to compute expectation values.
- Observables that do not commute with the Hamiltonian pose challenges.
- Descendant weighting and forward walking are techniques to address these challenges.
Purpose of the Study:
- To investigate the influence of population size on DQMC accuracy.
- To determine the relationship between population size and dimensionality.
- To identify conditions leading to systematic biases in DQMC simulations.
Main Methods:
- Simulations were performed on a d-dimensional isotropic harmonic oscillator model system.
- Descendant weighting technique was employed.
- Expectation values of non-commuting observables were computed.
Main Results:
- A rapid increase in population size is required with increasing dimensionality (d).
- Small population sizes result in significant systematic biases.
- Accuracy is strongly dependent on population size relative to system complexity.
Conclusions:
- Population size is a crucial parameter for reliable DQMC simulations.
- Careful consideration of population size is necessary, particularly for high-dimensional systems.
- Biases in DQMC results can be mitigated by adequately scaling population size with dimensionality.
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