We present a combination of quantum Monte Carlo methods and a finite-size extrapolation framework with which we calculate the thermodynamic limit of the exact correlation energy of the polarized electron gas at high densities to meV accuracy, $\ensuremath{-}40.44(5)$ and $\ensuremath{-}31.70(4)$ mHa at
rs=0.5 and 1, respectively. The fixed-node error is characterized and found to exceed 1 mHa, and we show that the magnitude of the correlation energy of the polarized electron gas is underestimated by up to 6 meV by the Perdew-Wang parametrization, for which we suggest improvements.
We investigate how the fixed-node diffusion Monte Carlo energy of solids depends on single-particle orbitals used in Slater-Jastrow wave functions. We demonstrate that the dependence can be significant, in particular in the case of
3d transition-metal compounds, which we adopt as examples. We illustrate how exchange-correlation functionals with variable exact-exchange component can be exploited to reduce the fixed-node errors. On the basis of these results we argue that the fixed-node quantum Monte Carlo provides a variational approach for optimization of effective single-particle Hamiltonians with parameters.
We calculate the ground-state properties of an unpolarized two-component Fermi gas with the aid of the diffusion quantum Monte Carlo (DMC) methods. Using an extrapolation to the zero effective range of the attractive two-particle interaction, we find
E/Efree in the unitary limit to be 0.212(2), 0.407(2), 0.409(3), and 0.398(3) for 4, 14, 38, and 66 atoms, respectively. Our calculations indicate that the dependence of the total energy on the effective range of the interaction
Reff is sizable and the extrapolation to
Reff=0 is therefore important for reaching the true unitary limit. To test the quality of nodal surfaces and to estimate the impact of the fixed-node approximation, we perform released-node DMC calculations for 4 and 14 atoms. Analysis of the released-node and the fixed-node results suggests that the main sources of the fixed-node errors are long-range correlations, which are difficult to sample in the released-node approaches due to the fast growth of the bosonic noise. Besides energies, we evaluate the two-body density matrix and the condensate fraction. We find that the condensate fraction for the 66-atom system converges to 0.56(1) after the extrapolation to the zero interaction range.