Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices

TL;DR

This paper combines Bethe-Ansatz-based density-functional theory with quantum Monte Carlo simulations to accurately study the ground-state properties of strongly correlated one-dimensional ultracold fermions in optical lattices, revealing detailed density profiles and correlation effects.

Contribution

It introduces a Bethe-Ansatz-based local-density approximation within density-functional theory and compares it with other approximations and simulations for confined 1D fermionic systems.

Findings

Bethe-Ansatz-based LDA accurately captures Luttinger-liquid and Mott-insulator physics.

Quantum Monte Carlo validates the reliability of the density-functional approximations.

Detailed atom-density profiles reveal the effects of interactions and confinement.

Abstract

We present an extensive numerical study of ground-state properties of confined repulsively interacting fermions on one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe-Ansatz-based local-density approximation for the correlation energy, which accounts for Luttinger-liquid and Mott-insulator physics. Semi-analytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-like local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these allow to obtain a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.