Self-healing diffusion quantum Monte Carlo algorithms: direct reduction of the fermion sign error in electronic structure calculations
- ORNL
- Lawrence Livermore National Laboratory (LLNL)
We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground state probability density. We take advantage of a basic property of the walker configuration distribution function generated in a DMC calculation, to i) project-out a multi-determinant expansion of the fixed node ground state wave-function and ii) to define a cost function that relates the interacting-ground-state-fixed-node and the non-interacting-trial wave-functions. We argue in favor of the conjecture that removing the kink of the fixed-node ground-state wave-function at the node improves the resulting wave-function nodal structure. If this conjecture is valid, then the noise in the fixed-noded wave function resulting from finite sampling would play a beneficial role, allowing the nodes to adjust towards the ones of the exact many-body ground state in a simulated annealing-like process. Based on these conjectures, we propose a method to improve both single determinant and multi-determinant expressions of the trial wave-function that can be generalized to other wave-function forms such as pfaffians. We test the method in a model system where a near analytical solution can be found. Comparing the DMC calculations with the exact solutions, we find that the trial wave-function is systematically improved. The overlap of the optimized trial wave-function and the exact ground state converges to 100\% even starting from wave-functions orthogonal to the exact ground state. Similarly, the DMC total energy and density converges to the exact solutions for the model. In the optimization process we find an approximation optimal effective non-interacting density-functional-like nodal potential whose existence was predicted in a previous publication [Phys. Rev. B 77 245110 (2008)]. Tests of the method are extended to a model system with a full Coulomb interaction where we show we can obtain the exact Kohn-Sham effective potential from the DMC data.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences (CNMS)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- DE-AC05-00OR22725
- OSTI ID:
- 1004421
- Journal Information:
- Physical Review B, Vol. 79, Issue 19; ISSN 1098--0121
- Country of Publication:
- United States
- Language:
- English
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