The fourth- and fifth-order virial coefficients from weak-coupling to unitarity

Abstract

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.

arXiv comment6 pages, 2 figures

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• The virial expansion of attractively interacting Fermi gases in 1D, 2D, and 3D, up to fifth order
• Fourth- and fifth-order virial expansion of harmonically trapped fermions at unitarity
• From weak to strong: constrained extrapolation of perturbation series with applications to dilute Fermi systems
• Thermodynamics of rotating quantum matter in the virial expansion
• Constrained extrapolation problem and order-dependent mappings
• Fourth cluster and virial coefficients of a unitary Fermi gas for an arbitrary mass ratio
• Toward an automated-algebra framework for high orders in the virial expansion of quantum matter
• The thermal index of neutron-star matter in the virial approximation