Constrained Path Monte Carlo method for spin $ 1/2 $ fermions at unitarity limit

TL;DR

This paper uses the constrained-path Monte Carlo method to calculate the ground-state energy of spin 1/2 fermions at the unitarity limit, providing results consistent with experimental and other computational approaches.

Contribution

It introduces a detailed Monte Carlo calculation for fermions at unitarity, including extrapolation to the thermodynamic limit and analysis of effective range effects.

Findings

Ground-state energy ratio to free Fermi gas: 0.43(4)

Results consistent with experimental and other Monte Carlo methods

Energy shows linear dependence on Fermi momentum and effective range

Abstract

We present calculations for spin $ 1/2 $ fermions at unitarity limit, where the effective range of the interaction is zero and the scattering length is infinite. We compute the ground-state energy for a system of 6, 10,14,18 and 20 particles, with equal numbers of up and down spins in a periodic cube in the full ground-state constrained-path Monte Carlo (CPMC) method using the extended, attractive Hubbard model. Our results in a careful extrapolation to the thermodynamic limit may suggest that the ratio of the ground-state energy to that of a free Fermi gas is $ \xi = 0.43(4) $, which can compare with recent experimental results and consistent with the fixed node Green's function Monte Carlo and novel lattice approaches results. We also obtain results for interactions with different effective ranges and find that the energy is consistent with a universal linear dependence on the product of the Fermi momentum and the effective range.