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Symmetry-Projected Jastrow Mean-Field Wave Function in Variational Monte Carlo
Ankit Mahajan1, Sandeep Sharma1
1Department of Chemistry and Biochemistry , University of Colorado Boulder , Boulder , Colorado 80302 , United States.
The Journal of Physical Chemistry. A
|April 5, 2019
Summary
We developed a low-scaling variational Monte Carlo (VMC) algorithm to optimize symmetry-projected Jastrow mean-field (SJMF) wave functions. This method efficiently captures electron correlation for various quantum systems.
Area of Science:
- Quantum Chemistry
- Computational Physics
Background:
- Variational Monte Carlo (VMC) methods are crucial for quantum many-body problems.
- Optimizing wave functions is key to accurately describing electron correlation.
- Existing methods can be computationally expensive for complex systems.
Purpose of the Study:
- To extend a low-scaling VMC algorithm for optimizing symmetry-projected Jastrow mean-field (SJMF) wave functions.
- To demonstrate the algorithm's efficiency and accuracy on benchmark systems.
- To enable calculation of reduced density matrices and other observables.
Main Methods:
- Developed a low-scaling VMC algorithm.
- Implemented optimization for SJMF wave functions, including Jastrow antisymmetrized geminal power and Jastrow-Pfaffians.
- Applied the method to nitrogen molecule, hydrogen chains, and the 2D Hubbard model.
Main Results:
- Achieved significant electron correlation capture with SJMF wave functions.
- Demonstrated computational efficiency even when breaking multiple symmetries (spin, particle number, etc.).
- Showed that reduced density matrices and correlation functions can be calculated.
Conclusions:
- The optimized SJMF wave functions provide a cost-effective way to obtain substantial electron correlation.
- The algorithm facilitates the calculation of various observables.
- This work enables integration of VMC within complete active-space self-consistent field (CASSCF) calculations.
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