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 temperatures, 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. By means of these factorizations and automated algebra codes, we obtain the interaction-induced change Δb n from weak coupling to unitarity. At unitarity, we find that Δb 3 ¼ −0.356ð4Þ in agreement with previous results, Δb 4 ¼ 0.062ð2Þ, which is in agreement with all previous theoretical estimates but at odds with experimental determinations, and Δb 5 ¼ 0.078ð6Þ, which is a prediction. We show the impact of those answers on the density equation of state and Tan contact, and trace their origin back to their polarized and unpolarized components.
Following up on recent calculations, we investigate the 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-order virial coefficient as a renormalization condition, we derive expressions for up to the seventh-order virial coefficient ∆b7. Our results, though approximate, furnish simple analytic formulas that relate ∆bn to ∆b2 for arbitrary dimension, providing a glimpse into the behavior of the virial expansion across dimensions and coupling strengths. As an application, we calculate the pressure and Tan's contact of the 2D attractive Fermi gas.
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