The variational and diffusion quantum Monte Carlo methods are used to calculate the correlation energy of the paramagnetic three-dimensional homogeneous electron gas at intermediate to high density. Ground-state energies in finite cells are determined using Slater-Jastrow-backflow trial wave functions, and finite-size errors are removed using twist-averaged boundary conditions and extrapolation of the energy per particle to the thermodynamic limit of infinite system size. Our correlation energies in the thermodynamic limit are more accurate than previous results. The present diffusion quantum Monte Carlo energies together with our recently reported [Phys. Rev. B 105, 245135 (2022)] results at low density, are used to parametrize the correlation energy of the electron gas using a functional form that satisfies the exact asymptotic behavior at high density.
Variational and diffusion quantum Monte Carlo (VMC and DMC) methods with Slater-Jastrow-backflow trial wave functions are used to study the spin-polarized three-dimensional uniform electron fluid. We report ground state VMC and DMC energies in the density range $0.5\ensuremath{\le}{r}_{\text{s}}\ensuremath{\le}20$. Finite-size errors are corrected using canonical-ensemble twist-averaged boundary conditions and extrapolation of the twist-averaged energy per particle calculated at three system sizes
(N=113,259,and387) to the thermodynamic limit of infinite system size. The DMC energies in the thermodynamic limit are used to parametrize a local spin density approximation correlation function for inhomogeneous electron systems.
We have studied the spin-polarized three-dimensional homogeneous electron gas using the diffusion quantum Monte Carlo method, with trial wave functions including backflow and three-body correlations in the Jastrow factor, and we have used twist averaging to reduce finite-size effects. Calculations of the pair-correlation function, including the on-top pair density, as well as the structure factor and the total energy, are reported for systems of 118 electrons in the density range
rs=0.5--20 a.u., and for spin polarizations of 0, 0.34, 0.66, and 1. We consider the spin resolution of the pair-correlation function and structure factor, and the energy of spin polarization. We show that a control variate method can reduce the variance when twist averaging, and we have achieved higher accuracy and lower noise than earlier quantum Monte Carlo studies.
Single-particle finite-size errors remain a central obstacle in quantum Monte Carlo (QMC) simulations of periodic systems, conventionally reduced via twist averaging (TA). Here we introduce Good-
Γ (GG) particle numbers as system sizes
N at which the
Γ-point Hartree--Fock (HF) energy of the high-density two-dimensional uniform electron gas (2D UEG) lies anomalously close to its thermodynamic-limit (TL) value. All results in this work concern the 2D UEG in its high-density Fermi-liquid regime,
rs=1--
4. We systematically investigate the kinetic- and exchange-energy errors,
ΔKE(N) and
ΔEX(N), that underlie this one-body finite-size-error cancellation across four densities and both spin polarizations. We then compare diffusion Monte Carlo (DMC) energies extrapolated to the TL from GG-
N sequences against twist-averaged extrapolations at the same densities and polarizations, finding agreement to within a fraction of a millihartree in every case, independent of whether a
1/N or an
N−5/4 extrapolation form is used.
Ab initio quantum Monte Carlo methods, in principle, allow for the calculation of exact properties of correlated many-electron systems but are, in general, limited to the simulation of a finite number of electrons N under periodic boundary conditions. Therefore, an accurate theory of finite-size effects is indispensable to bridge the gap to realistic applications in the thermodynamic limit. In this work, we revisit the uniform electron gas at finite temperature, as it is relevant to contemporary research, e.g., in the field of warm dense matter. In particular, we present a new scheme to eliminate finite-size effects both in the static structure factor S(q) and in the interaction energy v, which is based on the density response formalism. We demonstrate that this method often allows us to obtain v in the thermodynamic limit within a relative accuracy of ∼0.2% from as few as N = 4 electrons without any empirical choices or knowledge of results for other values of N. Finally, we evaluate the applicability of our method upon increasing the density parameter rs and decreasing the temperature T.
We show that known or knowable information about the high-$({r}_{s}\ensuremath{\rightarrow}0)$ and low-density $({r}_{s}\ensuremath{\rightarrow}\ensuremath{\infty})$ asymptotes can be used to predict the correlation energy per electron, ${e}_{c}({r}_{s},\ensuremath{\zeta})$, of the three-dimensional uniform gas over the whole range of the density parameter $(0\ensuremath{\le}{r}_{s}<\ensuremath{\infty})$ and relative spin polarization $(0\ensuremath{\le}|\ensuremath{\zeta}|\ensuremath{\le}1)$, without quantum Monte Carlo or other input. For $\ensuremath{\zeta}=0$, the high-density limit through order
rs is known exactly from many-body perturbation theory, and for all $\ensuremath{\zeta}$, the low-density limit through order
1/rs2 is known accurately from a simple, intuitive, and accurate model. We propose a single interpolation formula with the expected analytic structure to all orders in both limits, and use it to predict
ec(rs,0) in excellent agreement with quantum Monte Carlo data. For $|\ensuremath{\zeta}|>0$, we derive the $\ensuremath{\zeta}$ dependence of the coefficient ${a}_{1}(\ensuremath{\zeta})$ of the
rs ln rs term, previously known only for $|\ensuremath{\zeta}|=0$ and 1. For ${b}_{1}(\ensuremath{\zeta})$, the coefficient of the
rs term (not yet derived for $\ensuremath{\zeta}\ensuremath{\ne}0$), we approximately extend the known
b1(0) by using a simplification of the available quantum Monte Carlo information that replaces the second-order transition over
50<rs<100 by a sudden transition to full spin polarization at
rs=75.