2010/04/23 by Dominik Muth, Michael Fleischhauer, Bernd Schmidt
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum many-body systems #Quantum, superfluid, helium dynamics #cond-mat.quant-gas #physics.comp-ph #quant-ph
paper · pdf · doi:10.1103/physreva.82.013602
published as Phys. Rev. A 82, 013602 (2010) · 7 pages, 5 figures
arxiv created 2010/04/23 · openalex publication_date 2010/07/06 · arxiv updated 2010/09/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We present a general mapping between continuous and lattice models of Bose and Fermi gases in one dimension, interacting via local two-body interactions. For s-wave interacting bosons we arrive at the Bose-Hubbard model in the weakly interacting, low-density regime. The dual problem of p-wave interacting fermions is mapped to the spin-1/2 XXZ model close to the critical point in the highly polarized regime. The mappings are shown to be optimal in the sense that they produce the least error possible for a given discretization length. As an application we examine the ground state of an interacting Fermi gas in a harmonic trap, calculating numerically real-space and momentum-space distributions as well as two-particle correlations. In the analytically known limits the convergence of the results of the lattice model with the continuous one is shown.