Precision benchmark calculations for four particles at unitarity

TL;DR

This paper provides highly precise benchmark calculations for the ground state energy of a four-particle fermionic system at unitarity using three different ab initio methods, demonstrating consistent results across approaches.

Contribution

It introduces and compares three advanced ab initio computational methods for accurately calculating properties of particles at unitarity, achieving consistent benchmark results.

Findings

Ground state energy fractions around 0.21 for four particles at unitarity.

Good agreement among Hamiltonian lattice, Euclidean lattice, and diffusion Monte Carlo methods.

Minimal energy decrease in released-node calculations confirms stability of fixed-node results.

Abstract

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, and continuum diffusion Monte Carlo 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 non-interacting system. We obtain values 0.211(2) and 0.210(2) using two different Hamiltonian lattice representations, 0.206(9) using Euclidean lattice, and an upper bound of 0.212(2) from fixed-node diffusion Monte Carlo. 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 in Euclidean time, where E_F is the Fermi energy. We find good agreement among all three ab initio methods.