Exact numerical simulations of interacting fermions in 1D trapping potentials

We discuss p-wave interacting spin-polarized fermions in a 1D trapping potential for arbitrary interaction strength. Using a boson-fermion mapping in 1D, interacting fermions with p-wave interaction strength $g_{1D}^F$ can be mapped to bosons with s-wave interaction strength $g_{1D}^B$ = -1/g$_{1D}^F$. As a consequence a weakly interacting Fermi gas behaves in local properties like a strongly interacting Bose gas and vice versa. We derive a proper discretized model for the interacting fermions and compare its predictions with that obtained by the Bose-Fermi mapping using DMRG and TEBD simulations. We calculate the realspace and momentum distributions of the fermions for the whole range of interaction strength starting at a weakly interacting gas going to the Fermi-Tonks limit and compare the results to predictions from field theoretical approaches.