Physics – Quantum Physics
Scientific paper
2010-04-23
Phys. Rev. A 82, 013602 (2010)
Physics
Quantum Physics
7 pages, 5 figures
Scientific paper
10.1103/PhysRevA.82.013602
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 a 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 to the continuous one is shown.
Fleischhauer Michael
Muth Dominik
Schmidt Bernd
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