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.

6 pages, 2 figures

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Nonrelativistic conformal field theories
• Epsilon expansion for a Fermi gas at infinite scattering length
• Viscosity and scale invariance in the unitary Fermi gas
• Virial expansion for a strongly correlated Fermi gas
• Spectral response and contact of the unitary Fermi gas
• Universal contact of strongly interacting fermions at finite temperatures
• Contact and sum-rules in a near-uniform Fermi gas at unitarity
• Temperature and coupling dependence of the universal contact intensity for an ultracold Fermi gas
• The Neutrino Response of Low-Density Neutron Matter from the Virial Expansion
• Next-to-next-to-leading-order epsilon expansion for a Fermi gas at infinite scattering length
• High-temperature limit of the resonant Fermi gas

Cited by in corpus (2)

• Thermodynamics of rotating quantum matter in the virial expansion
• Constrained extrapolation problem and order-dependent mappings