Gridbased diffusion Monte Carlo for fermions without the fixednode approximation
Abstract
A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a fewfermion system and its groundstate energy without an uncontrolled bias. This is achieved by confining signed random walkers to the points of a uniform infinite spatial grid, allowing them to meet and annihilate one another to establish the nodal structure without the fixednode approximation. An imaginarytime propagator is derived rigorously from a discretized Hamiltonian, governing a nonGaussian, signflipping, branching, and mutually annihilating random walk of particles. The accuracy of the resulting stochastic representations of a fermion wave function is limited only by the grid and imaginarytime resolutions and can be improved in a controlled manner. Here, the method is tested for a series of model problems including fermions in a harmonic trap as well as the He atom in its singlet or triplet ground state. For the latter case, the energies approach from above with increasing grid resolution and converge within 0.015 E_{h} of the exact basissetlimit value for the grid spacing of 0.08 a.u. with a statistical uncertainty of 10^{–5} E_{h} without an importance sampling or Jastrow factor.
 Authors:

 Univ. of Illinois at UrbanaChampaign, IL (United States)
 Publication Date:
 Research Org.:
 Univ. of Illinois at UrbanaChampaign, IL (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES)
 OSTI Identifier:
 1594980
 Grant/Contract Number:
 SC0006028
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review E
 Additional Journal Information:
 Journal Volume: 101; Journal Issue: 1; Journal ID: ISSN 24700045
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS
Citation Formats
Kunitsa, Alexander A., and Hirata, So. Gridbased diffusion Monte Carlo for fermions without the fixednode approximation. United States: N. p., 2020.
Web. doi:10.1103/PhysRevE.101.013311.
Kunitsa, Alexander A., & Hirata, So. Gridbased diffusion Monte Carlo for fermions without the fixednode approximation. United States. doi:10.1103/PhysRevE.101.013311.
Kunitsa, Alexander A., and Hirata, So. Mon .
"Gridbased diffusion Monte Carlo for fermions without the fixednode approximation". United States. doi:10.1103/PhysRevE.101.013311. https://www.osti.gov/servlets/purl/1594980.
@article{osti_1594980,
title = {Gridbased diffusion Monte Carlo for fermions without the fixednode approximation},
author = {Kunitsa, Alexander A. and Hirata, So},
abstractNote = {A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a fewfermion system and its groundstate energy without an uncontrolled bias. This is achieved by confining signed random walkers to the points of a uniform infinite spatial grid, allowing them to meet and annihilate one another to establish the nodal structure without the fixednode approximation. An imaginarytime propagator is derived rigorously from a discretized Hamiltonian, governing a nonGaussian, signflipping, branching, and mutually annihilating random walk of particles. The accuracy of the resulting stochastic representations of a fermion wave function is limited only by the grid and imaginarytime resolutions and can be improved in a controlled manner. Here, the method is tested for a series of model problems including fermions in a harmonic trap as well as the He atom in its singlet or triplet ground state. For the latter case, the energies approach from above with increasing grid resolution and converge within 0.015 Eh of the exact basissetlimit value for the grid spacing of 0.08 a.u. with a statistical uncertainty of 10–5 Eh without an importance sampling or Jastrow factor.},
doi = {10.1103/PhysRevE.101.013311},
journal = {Physical Review E},
number = 1,
volume = 101,
place = {United States},
year = {2020},
month = {1}
}
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