Density functional theory versus quantum Monte Carlo simulations of Fermi gases in the optical-lattice arena

TL;DR

This study compares density functional theory and quantum Monte Carlo simulations for Fermi gases in optical lattices, highlighting the accuracy and limitations of DFT's local spin-density approximation across different interaction regimes and dimensions.

Contribution

It provides benchmark data for DFT and DMC methods in optical lattices, demonstrating LSDA's accuracy and identifying its limitations near strong interactions and deep lattices.

Findings

LSDA is highly accurate in weak and intermediate interactions

LSDA has limitations near the Tonks-Girardeau limit and deep lattices

One-dimensional data serve as benchmarks for future DFT development

Abstract

We benchmark the ground state energies and the density profiles of atomic repulsive Fermi gases in optical lattices computed via Density Functional Theory (DFT) against the results of diffusion Monte Carlo (DMC) simulations. The main focus is on a half-filled one-dimensional optical lattices, for which the DMC simulations performed within the fixed-node approach provide unbiased results. This allows us to demonstrate that the local spin-density approximation (LSDA) to the exchange-correlation functional of DFT is very accurate in the weak and intermediate interactions regime, and also to underline its limitations close to the strongly-interacting Tonks-Girardeau limit and in very deep optical lattices. We also consider a three dimensional optical lattice at quarter filling, showing also in this case the high accuracy of the LSDA in the moderate interaction regime. The one-dimensional data provided in this study may represent a useful benchmark to further develop DFT methods beyond the LSDA and they will hopefully motivate experimental studies to accurately measure the equation of state of Fermi gases in higher-dimensional geometries.