One-dimensional harmonically confined SU(N) fermions

We study the momentum distributions and spatial correlations of few harmonically confined SU(N) fermions using quantum Monte Carlo methods. In our study, we vary the spin degeneracy N from 2 to 6 and the total number of particles from 6 to 18. Only balanced mixtures, with the same number of atoms per spin type, and repulsive unlike-spin contact interactions are considered. Going from N=2 to N=6, with the same occupancy of each spin state, we observe an increase of atom-atom correlations. This effect is particularly significant in the momentum distributions, which show fatter tails at large k (ks>5, s being the oscillator length) when N grows, in agreement with experimental findings. Those tails also show the expected k-4 decay related to the Tan contact for different values of the spin degeneracy. According to our results, the local spin ordering and the spin-spin correlations are mainly determined by N via the Pauli exclusion principle, with minor influences from the particle-particle interactions, irrespective of the total number of confined atoms.Postprint (published version