Path-Integral Monte Carlo Determination of the Fourth-Order Virial Coefficient for a Unitary Two-Component Fermi Gas with Zero-Range Interactions

The unitary equal-mass Fermi gas with zero-range interactions constitutes a paradigmatic model system that is relevant to atomic, condensed matter, nuclear, particle, and astrophysics. This work determines the fourth-order virial coefficient b(4) of such a strongly interacting Fermi gas using a customized ab initio path-integral Monte Carlo (PIMC) algorithm. In contrast to earlier theoretical results, which disagreed on the sign and magnitude of b(4), our b(4) agrees within error bars with the experimentally determined value, thereby resolving an ongoing literature debate. Utilizing a trap regulator, our PIMC approach determines the fourth-order virial coefficient by directly sampling the partition function. An on-the-fly antisymmetrization avoids the Thomas collapse and, combined with the use of the exact two-body zero-range propagator, establishes an efficient general means to treat small Fermi systems with zero-range interactions.