Grid-based diffusion Monte Carlo for fermions without the fixed-node approximation

Kunitsa, Alexander A.; Hirata, So

doi:10.1103/PhysRevE.101.013311

Grid-based diffusion Monte Carlo for fermions without the fixed-node approximation

Journal Article · Mon Jan 27 00:00:00 EST 2020 · Physical Review E

DOI:https://doi.org/10.1103/PhysRevE.101.013311· OSTI ID:1594980

^[1]; ^[2]

Univ. of Illinois at Urbana-Champaign, IL (United States); University of Illinois at Urbana-Champaign
Univ. of Illinois at Urbana-Champaign, IL (United States)

A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a few-fermion system and its ground-state 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 fixed-node approximation. An imaginary-time propagator is derived rigorously from a discretized Hamiltonian, governing a non-Gaussian, sign-flipping, 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 imaginary-time 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 basis-set-limit 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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0006028

OSTI ID:: 1594980

Journal Information:: Physical Review E, Journal Name: Physical Review E Journal Issue: 1 Vol. 101; ISSN PLEEE8; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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