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Grid-based diffusion Monte Carlo for fermions without the fixed-node approximation
- Publication Year :
- 2018
-
Abstract
- 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. 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 0.015E_{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.
- Subjects :
- Physics
Quantum Physics
FOS: Physical sciences
Propagator
Fermion
Computational Physics (physics.comp-ph)
Random walk
Grid
01 natural sciences
010305 fluids & plasmas
symbols.namesake
0103 physical sciences
symbols
Diffusion Monte Carlo
Statistical physics
Quantum Physics (quant-ph)
010306 general physics
Hamiltonian (quantum mechanics)
Wave function
Physics - Computational Physics
Importance sampling
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....a1b112559ee955e62a87754cecce4bb9