Ground-state energy, density profiles, and momentum distribution of attractively interacting 1D Fermi gases with hard-wall boundaries: a Monte Carlo study
| Autor: | McKenney, J. R., Shill, C. R., Porter, W. J., Drut, J. E. |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | J. Phys. B 49, 225001 (2016) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/0953-4075/49/22/225001 |
| Popis: | Motivated by the realization of hard-wall boundary conditions in experiments with ultracold atoms, we investigate the ground-state properties of spin-1/2 fermions with attractive interactions in a one-dimensional box. We use lattice Monte Carlo methods to determine essential quantities like the energy, which we compute as a function of coupling strength and particle number in the regime from few to many particles. Many-fermion systems bound by hard walls display non-trivial density profiles characterized by so-called Friedel oscillations (which are similar to those observed in harmonic traps). In non-interacting systems, the characteristic length scale of the oscillations is set by (2 kF)^(-1), where kF is the Fermi momentum, while repulsive interactions tend to generate Wigner-crystal oscillations of period (4 kF)^(-1). Based on the non-interacting result, we find a remarkably simple parametrization of the density profiles of the attractively interacting case, which we generalize to the one-body density matrix. While the total momentum is not a conserved quantity in the presence of hard walls, the magnitude of the momentum does provide a good quantum number. We are therefore able to provide a detailed characterization of the (quasi-)momentum distribution, which displays rather robust discontinuity at the Fermi surface. In addition, we determine the spatially varying on-site density-density correlation, which in turn yields Tan's contact density and, upon integration, Tan's contact. As is well known, the latter fully determines the short-range correlations and plays a crucial role in a multitude of equilibrium and non-equilibrium sum rules. Comment: 9 pages, 8 figures. Results unchanged; major improvements to text; new data on one-body density matrix, on-site correlations, and Tan's contact density with corresponding analysis |
| Databáze: | arXiv |
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