Momentum Distribution and Contact of the Unitary Fermi gas

TL;DR

This paper uses Quantum Monte Carlo methods to analyze the momentum distribution and contact parameter of the Unitary Fermi Gas at various temperatures, confirming Tan relations and revealing temperature dependence of the contact.

Contribution

It provides the first finite-temperature Quantum Monte Carlo calculations of the momentum distribution and contact for the Unitary Fermi Gas, including temperature dependence.

Findings

n(k) follows C/k^4 at large momenta, consistent with Tan relations.

The contact C increases with temperature up to a maximum around T/ε_F ≈ 0.4.

Results are obtained on lattices up to N_x=14 with low particle density.

Abstract

We calculate the momentum distribution n(k) of the Unitary Fermi Gas using Quantum Monte Carlo calculations at finite temperature T/\epsilon_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/\epsilon_F and present a comparison with theory. At low T/\epsilon_F, we find that C increases with temperature, and we tentatively identify a maximum around T/\epsilon_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.