Resonantly Interacting Fermions In a Box

TL;DR

This paper combines Quantum Monte Carlo and Density Functional Theory to analyze finite-size effects in a unitary Fermi gas within a periodic box, providing new bounds on its ground-state energy and insights into shell structures.

Contribution

It introduces a new DFT functional that captures finite-size effects and extrapolates QMC results to the thermodynamic limit, offering the tightest energy bounds to date.

Findings

Shell structure vanishes for systems with more than 50 particles.

The DFT accurately predicts finite-size effects and matches QMC results.

Provides a new upper bound on the ground-state energy of the unitary gas.

Abstract

We use two fundamental theoretical frameworks to study the finite-size (shell) properties of the unitary gas in a periodic box: 1) an ab initio Quantum Monte Carlo (QMC) calculation for boxes containing 4 to 130 particles provides a precise and complete characterization of the finite-size behavior, and 2) a new Density Functional Theory (DFT) fully encapsulates these effects. The DFT predicts vanishing shell structure for systems comprising more than 50 particles, and allows us to extrapolate the QMC results to the thermodynamic limit, providing the tightest bound to date on the ground-state energy of the unitary gas: \xi_S <= 0.383(1). We also apply the new functional to few-particle harmonically trapped systems, comparing with previous calculations.