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A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations
Phani K V V Nukala1, P R C Kent
1Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6164, USA.
The Journal of Chemical Physics
|June 3, 2009
Summary
We developed a new algorithm for quantum Monte Carlo (QMC) simulations that significantly speeds up calculations. This method efficiently updates trial wave functions, reducing computational cost and enabling more accurate simulations.
Area of Science:
- Computational Physics
- Quantum Chemistry
Background:
- Quantum Monte Carlo (QMC) simulations are crucial for studying quantum systems.
- Updating trial wave functions is a computationally intensive step in QMC.
- Existing methods have limitations in efficiency, especially for complex wave functions.
Purpose of the Study:
- To present an efficient low-rank updating algorithm for trial wave functions in QMC.
- To reduce the computational complexity and storage requirements of QMC calculations.
- To enable more accurate and faster QMC simulations, particularly for multideterminant wave functions.
Main Methods:
- The algorithm employs low-rank updating of Slater determinants.
- It achieves a computational complexity of O(kN) per step, where N is system size.
- The method is applied to both single-determinant and multideterminant trial wave functions.
Main Results:
- The new algorithm is faster than the traditional Sherman-Morrison algorithm for single determinants up to O(N) updates.
- For multideterminant configuration-interaction wave functions, it offers significant savings in work and storage (O(MN(2))).
- The efficiency gains are substantial for complex wave functions with M+1 determinants.
Conclusions:
- The developed low-rank updating algorithm provides a significant efficiency improvement for QMC simulations.
- It makes QMC calculations using configuration-interaction wave functions more feasible and accurate.
- This advancement can accelerate research in various quantum mechanical systems.
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