Thermal distribution and the contact of Fermi gases at large scattering lengths

A few years ago, Tan and others derived a set of exact relations valid for strongly interacting non-relativistic Fermi gases in the regime of short interaction range and large scattering length. Recent developments have shown that a central quantity in these identities, the so-called ``contact'' C, actually plays a crucial role in the characterization of these systems, as it determines multiple thermodynamic properties as well as linear-response sum rules. However, computing the ``contact'' presents a challenge as it requires non-perturbative methods such as Quantum Monte Carlo. In this contribution, we present our first results for C as a function of temperature in the limit of infinite scattering length.