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

Gao Xianlong·Marco Polini·M. P. Tosi·Vivaldo L. Campo, Jr.·Klaus Capelle·Marcos Rigol
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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.

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Gao Xianlong, Marco Polini, M. P. Tosi, Vivaldo L. Campo, Jr., Klaus Capelle, Marcos Rigol. 2005-12-08. Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices. https://doi.org/10.1103/physrevb.73.165120

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