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The contact in the unitary Fermi gas across the superfluid phase transition

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.