Exponentially Decaying Correlations in a Gas of Strongly Interacting Spin-Polarized 1D Fermions with Zero-Range Interactions

We consider the single-particle correlations and momentum distributions in a gas of strongly interacting, spinless 1D fermions with zero-range interactions. This system represents a fermionic version of the Tonks-Girardeau gas of impenetrable bosons as it can be mapped to a system of noninteracting 1D bosons. We use this duality to show that the T=0, single-particle correlations exhibit an exponential decay with distance. This strongly interacting system is experimentally accessible using ultracold atoms and has a Lorentzian momentum distribution at large momenta whose width is given by the linear density.