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

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.

8 pages, 7 figures, plus supplemental material (1 page). Typos corrected

References in corpus (9)

• Many-Body Physics with Ultracold Gases
• Exact solution for infinitely strongly interacting Fermi gases in tight waveguides
• Exact quantum Monte Carlo study of one dimensional trapped fermions with attractive contact interactions
• Exploring the ferromagnetic behaviour of a repulsive Fermi gas via spin dynamics
• Emergence of Wigner molecules in one-dimensional systems of repulsive fermions under harmonic confinement
• One-dimensional multicomponent Fermi gas in a trap: quantum Monte Carlo study
• Itinerant ferromagnetism in a Fermi gas with contact interaction: Magnetic properties in a dilute Hubbard model
• One-dimensional Repulsive Fermi Gas in a Tunable Periodic Potential
• Kohn-Sham approach to Fermi gas superfluidity: the bilayer of fermionic polar molecules

Cited by in corpus (4)

• Mott-Anderson Metal-Insulator Transitions from Entanglement
• Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids
• Asymptotics of eigenvalue sums when some turning points are complex
• Phase Transitions of Repulsive Two-Component Fermi Gases in Two Dimensions