Atomic Fermi gas at the unitary limit by quantum Monte Carlo methods: Effects of the interaction range

TL;DR

This study uses quantum Monte Carlo methods to analyze the ground-state properties of an unpolarized Fermi gas at the unitary limit, emphasizing the importance of interaction range extrapolation and assessing fixed-node errors.

Contribution

It provides detailed calculations of energy and condensate fraction for various atom numbers, highlighting the impact of interaction range and fixed-node approximation in quantum Monte Carlo simulations.

Findings

Energy ratios vary with atom number, emphasizing the importance of zero-range extrapolation.

Condensate fraction converges to approximately 0.56 for large systems.

Fixed-node errors are mainly due to long-range correlations, challenging to sample.

Abstract

We calculate the ground-state properties of unpolarized two-component Fermi gas by the diffusion quantum Monte Carlo (DMC) methods. Using an extrapolation to the zero effective range of the attractive two-particle interaction, we find $E/E_{\rm free}$ to be 0.212(2), 0.407(2), 0.409(3) and 0.398(3) for 4, 14, 38 and 66 atoms, respectively. Our results indicate that the dependence of the total energy on the effective range is sizable and the extrapolation is therefore quite important. In order 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.