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Momentum Distribution and Contact of the Unitary Fermi gas

We calculate the momentum distribution n(k) of the Unitary Fermi Gas 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/k^4, 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 \simeq 0.4. Our calculations are performed on lattices of spatial extent up to N_x = 14 with a particle number per unit volume of \simeq 0.03 - 0.07.