Spin-incoherent Luttinger liquid of one-dimensional SU( κ ) fermions

Abstract

We theoretically investigate one-dimensional (1D) $\mathrm{SU}(\ensuremath{\kappa}$) fermions in the regime of spin-incoherent Luttinger liquid. We specifically focus on the Tonks-Girardeau gas limit where its density is sufficiently low that effective repulsions between atoms become infinite. In such case, spin exchange energy of 1D $\mathrm{SU}(\ensuremath{\kappa}$) fermions vanishes and all spin configurations are degenerate, which automatically puts them into a spin-incoherent regime. In this limit, we are able to express the single-particle density matrices in terms of those of anyons. This allows us to numerically simulate the number of particles up to $N=32$. We numerically calculate single-particle density matrices in two cases: (1) equal populations for each spin components (balanced) and (2) all ${S}_{z}$ manifolds included. In contrast to noninteracting multicomponent fermions, the momentum distributions are broadened due to strong interactions. As $\ensuremath{\kappa}$ increases, the momentum distributions are less broadened for fixed $N$, while they are more broadened for fixed number of particles per spin component. We then compare numerically calculated high-momentum tails with analytical predictions which are proportional to $1/{p}^{4}$, in good agreement. Thus, our theoretical study provides a comparison with the experiments of repulsive multicomponent alkaline-earth fermions with a tunable $\mathrm{SU}(\ensuremath{\kappa}$) spin symmetry in the spin-incoherent regime.