  A quantity known as the contact plays a fundamental role in quantum many-body
systems with short-range interactions. The determination of the temperature
dependence of the contact for the unitary Fermi gas of infinite scattering
length has been a major challenge, with different calculations yielding
qualitatively different results. Here we use finite-temperature auxiliary-field
quantum Monte Carlo (AFMC) methods on the lattice within the canonical ensemble
to calculate the temperature dependence of the contact for the homogeneous
spin-balanced unitary Fermi gas. We extrapolate to the continuum limit for 40,
66, and 114 particles. We observe a dramatic decrease in the contact as the
superfluid critical temperature is approached from below, followed by a gradual
weak decrease as the temperature increases in the normal phase. Our results are
in excellent agreement with the most recent precision ultracold atomic gas
experiments. We also present results for the energy of the unitary gas as a
function of temperature in the continuum limit.
