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In the current era of precision quantum many-body physics, one of the most scrutinized systems is the unitary limit of the nonrelativistic spin-$1/2$ Fermi gas, due to its simplicity and relevance for atomic, condensed matter, and nuclear physics. The thermodynamics of this strongly correlated system is determined by universal functions which, at high temperature, are governed by universal virial coefficients $b_n$ that capture the effects of the $n$-body system on the many-body dynamics. Currently, $b_2$ and $b_3$ are well understood, but the situation is less clear for $b_4$, and no predictions have been made for $b_5$. To answer these open questions, we implement a nonperturbative analytic approach based on the Trotter-Suzuki factorization of the imaginary-time evolution operator, using progressively finer temporal lattice spacings. Implementing these factorizations and automated algebra codes, we obtain the interaction-induced change $Delta b_n$ from weak coupling to unitarity. At unitarity, we find: $Delta b_3 = -0.356(4)$, in agreement with previous results; $Delta b_4 = 0.062(2)$, in agreement with all previous theoretical estimates but at odds with experimental determinations; and $Delta b_5 = 0.078(6)$, which is a prediction. We show the impact of those answers on the density equation of state and Tan contact, and track their origin back to their polarized and unpolarized components.
By generalizing our automated algebra approach from homogeneous space to harmonically trapped systems, we have calculated the fourth- and fifth-order virial coefficients of universal spin-1/2 fermions in the unitary limit, confined in an isotropic ha
The virial expansion characterizes the high-temperature approach to the quantum-classical crossover in any quantum many-body system. Here, we calculate the virial coefficients up to the fifth-order of Fermi gases in 1D, 2D, and 3D, with attractive co
Using a leading-order semiclassical approximation, we calculate the third- and fourth-order virial coefficients of nonrelativistic spin-1/2 fermions in a harmonic trapping potential in arbitrary spatial dimensions, and as functions of temperature, tr
Using a coarse temporal lattice approximation, we calculate the first few terms of the virial expansion of a three-species fermion system with a three-body contact interaction in $d$ spatial dimensions, both in homogeneous space as well as in a harmo
Following up on recent calculations, we investigate the leading- and next-to-leading order semiclassical approximation to the virial coefficients of a two-species fermion system with a contact interaction. Using the analytic result for the second-ord