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arXiv:1801.02095 · The European Physical Journal B

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

Sebastiano Pilati, Ilia Zintchenko, Matthias Troyer, Francesco Ancilotto

Published Apr 1, 2018• 5 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2018-90021-1

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Using continuous-space quantum Monte Carlo methods, we investigate the zero-temperature ferromagnetic behavior of a two-component repulsive Fermi gas under the influence of periodic potentials that describe the effect of a simple-cubic optical lattice. Simulations are performed with balanced and with imbalanced components, including the case of a single impurity immersed in a polarized Fermi sea (repulsive polaron). For an intermediate density below half filling, we locate the transitions between the paramagnetic, and the partially and fully ferromagnetic phases. As the intensity of the optical lattice increases, the ferromagnetic instability takes place at weaker interactions, indicating a possible route to observe ferromagnetism in experiments performed with ultracold atoms. We compare our findings with previous predictions based on the standard computational method used in material science, namely density functional theory, and with results based on tight-binding models.
We present an extensive numerical study of the ground-state properties of confined repulsively interacting fermions in 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 that accounts for Luttinger-liquid and Mott-insulator physics. Semianalytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-type 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 provide a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.