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arXiv · 1004.4099

Discretized vs. continuous models of p-wave interacting fermions in 1D

Dominik Muth·Michael Fleischhauer·Bernd Schmidt
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Abstract

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.

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Dominik Muth, Michael Fleischhauer, Bernd Schmidt. 2010-04-23. Discretized vs. continuous models of p-wave interacting fermions in 1D. https://doi.org/10.1103/physreva.82.013602

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