@article{li_kolorenc_mitas_2011, title={Atomic Fermi gas in the unitary limit by quantum Monte Carlo methods: Effects of the interaction range}, volume={84}, ISSN={["1094-1622"]}, DOI={10.1103/physreva.84.023615}, abstractNote={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 $E/{E}_{\mathrm{free}}$ 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 ${R}_{\mathrm{eff}}$ is sizable and the extrapolation to ${R}_{\mathrm{eff}}=0$ 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.}, number={2}, journal={PHYSICAL REVIEW A}, author={Li, Xin and Kolorenc, Jindrich and Mitas, Lubos}, year={2011}, month={Aug} }
@article{bour_li_lee_meissner_mitas_2011, title={Precision benchmark calculations for four particles at unitarity}, volume={83}, ISSN={["1094-1622"]}, DOI={10.1103/physreva.83.063619}, abstractNote={The unitarity limit describes interacting particles where the range of the interaction is zero and the scattering length is infinite. We present precision benchmark calculations for two-component fermions at unitarity using three different ab initio methods: Hamiltonian lattice formalism using iterated eigenvector methods, Euclidean lattice formalism with auxiliary-field projection Monte Carlo methods, and continuum diffusion Monte Carlo methods with fixed and released nodes. We have calculated the ground-state energy of the unpolarized four-particle system in a periodic cube as a dimensionless fraction of the ground-state energy for the noninteracting system. We obtain values of $0.211(2)$ and $0.210(2)$ using two different Hamiltonian lattice representations, $0.206(9)$ using Euclidean lattice formalism, and an upper bound of $0.212(2)$ from fixed-node diffusion Monte Carlo methods. Released-node calculations starting from the fixed-node result yield a decrease of less than $0.002$ over a propagation of $0.4{E}_{F}^{\ensuremath{-}1}$ in Euclidean time, where ${E}_{F}$ is the Fermi energy. We find good agreement among all three ab initio methods.}, number={6}, journal={PHYSICAL REVIEW A}, author={Bour, Shahin and Li, Xin and Lee, Dean and Meissner, Ulf-G. and Mitas, Lubos}, year={2011}, month={Jun} }