Path integral Monte Carlo determination of the fourth-order virial coefficient for unitary two-component Fermi gas with zero-range interactions

Abstract

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 astro physics. This work determines the fourth-order virial coefficient $b_4$ of such a strongly-interacting Fermi gas using a customized \textit{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 anti-symmetrization 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.

5 pages (2 figures) + 5 pages (1 figure). Added a table, included more discussion about the fitted function, corrected a few typos, and updated Fig.2

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Virial expansion for a strongly correlated Fermi gas
• High-order Path Integral Monte Carlo methods for solving quantum dot problems
• High-temperature limit of the resonant Fermi gas
• Absence of a four-body Efimov effect in the 2 + 2 fermionic problem
• Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations
• Incorporating exact two-body propagators for zero-range interactions into $N$-body Monte Carlo simulations
• The third virial coefficient of a two-component unitary Fermi gas across an Efimov-effect threshold
• Temperature-dependence of small harmonically trapped atom systems with Bose, Fermi and Boltzmann statistics

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