Exponentially decaying correlations in a gas of strongly interacting spin-polarized 1D fermions with zero-range interactions

TL;DR

This paper investigates the decay of single particle correlations and momentum distribution in a strongly interacting 1D fermionic gas, revealing exponential correlations and a Lorentzian momentum profile, with implications for ultracold atom experiments.

Contribution

It demonstrates that strongly interacting 1D fermions exhibit exponential decay in correlations and a Lorentzian momentum distribution, utilizing a duality with bosonic systems.

Findings

Single particle correlations decay exponentially with distance.

Momentum distribution is Lorentzian at large momentum.

Correlation decay and momentum profile are experimentally relevant.

Abstract

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 momentum whose width is given by the linear density.