Eur. Phys. J. B (2018) 91: 70
https://doi.org/10.1140/epjb/e2018-90021-1

Regular Article

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

¹ Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova, via Marzolo 8, 35131 Padova, Italy
² School of Science and Technology, Physics Division, University of Camerino, Via Madonna delle Carceri 9, 62032 Camerino, Italy
³ Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
⁴ Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA, USA
⁵ CNR-IOM Democritos, via Bonomea 265, 34136 Trieste, Italy

^a e-mail: sebastiano.pilati@unicam.it

Received: 12 January 2018
Received in final form: 7 March 2018
Published online: 30 April 2018

Abstract

We benchmark the ground state energies and the density profiles of atomic repulsive Fermi gases in optical lattices (OLs) 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 OLs, 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 OLs. We also consider a three-dimensional OL 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.