Momentum Distribution and Contact of the Unitary Fermi Gas

We calculate the momentum distribution n(k) of the unitary Fermi gas by using quantum Monte Carlo calculations at finite temperature T/ϵ(F) as well as in the ground state. At large momenta k/k(F), we find that n(k) falls off as C/k⁴, in agreement with the Tan relations. From the asymptotics of n(k), we determine the contact C as a function of T/ϵ(F) and present a comparison with theory. At low T/ϵ(F), we find that C increases with temperature, and we tentatively identify a maximum around T/ϵ(F) ≃ 0.4. Our calculations are performed on lattices of spatial extent up to N(x) = 14 with a particle number per unit volume of ≃ 0.03-0.07.