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Restricted configuration path integral Monte Carlo | | A. Yilmaz
; K. Hunger
; T. Dornheim
; S. Groth
; M. Bonitz
; | | Date: |
24 Jul 2020 | | Abstract: | Quantum Monte Carlo belongs to the most accurate simulation techniques for
quantum many-particle systems. However, for fermions, these simulations are
hampered by the sign problem that prohibits simulations in the regime of strong
degeneracy. The situation changed with the development of configuration path
integral Monte Carlo (CPIMC) by Schoof extit{et al.} [T. Schoof extit{et
al.}, Contrib. Plasma Phys. extbf{51}, 687 (2011)] that allowed for the first
extit{ab initio} simulations for dense quantum plasmas. CPIMC also has a sign
problem that occurs when the density is lowered, i.e. in a parameter range that
is complementary to traditional QMC formulated in coordinate space. Thus, CPIMC
simulations for the warm dense electron gas are limited to small values of the
Brueckner parameter -- the ratio of the interparticle distance to the Bohr
radius -- $r_s=ar{r}/a_B lesssim 1$. In order to reach the regime of
stronger coupling (lower density) with CPIMC, here we investigate additional
restrictions on the Monte Carlo procedure. In particular, we introduce two
different versions of "restricted CPIMC" where certain sign changing Monte
Carlo updates are being omitted. Interestingly, one of the methods (RCPIMC) has
no sign problem at all, but it is less accurate than RCPIMC+ which neglects
only a smaller class of the Monte Carlo steps. Here we report extensive
simulations for the ferromagnetic uniform electron gas with which we
investigate the properties and accuracy of RCPIMC and RCPIMC+. Further, we
establish the parameter range in the density-temperature plane where these
simulations are both feasible and accurate. The conclusion is that RCPIMC and
RCPIMC+ work best at temperatures in the range of $Theta sim 0.1dots 0.5$
allowing to reach density parameters up to $r_s sim 3dots 5$, thereby
partially filling a gap left open by existing extit{ab initio} QMC methods. | | Source: | arXiv, 2007.12498 | | Services: | Forum | Review | PDF | Favorites | |
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