High-precision data for the unitary Fermi gas from diagrammatic series with zero convergence radius

In this talk I will mainly focus on the unitary Fermi gas (spin 1/2 fermions with contact interactions in 3D, which describes cold atomic gases at a Feshbach resonance) in the normal phase. Thanks to a diagrammatic Monte Carlo algorithm, we accurately sample all skeleton diagrams (built on dressed single-particle and pair propagators) up to order nine [1]. The diagrammatic series is divergent and there is no small parameter so that a resummation method is needed. We compute the large-order asymptotics of the diagrammatic series, based on a functional integral representation of the skeleton series and the saddle-point method. We show that the radius of convergence is actually zero, but the series is still resummable, by a generalised conformal-Borel transformation that incorporates the large-order asymptotics [2]. This yields new high-precision data, not only for the equation of state, but also for Tan's contact coefficient and for the momentum distribution [3]. I will also highlight some recent developments in (determinant) diagrammatic Monte Carlo and present new high-precision data for the Fermi polaron, which is a single impurity atom immersed in a Fermi sea.

References:

[1] K. Van Houcke, F. Werner, N. Prokof'ev, B. Svistunov, "Bold diagrammatic Monte Carlo for the resonant Fermi gas", arXiv:1305.3901
[2] R. Rossi, T. Ohgoe, K. Van Houcke, F. Werner, "Resummation of diagrammatic series with zero convergence radius for strongly correlated fermions", Phys. Rev. Lett. 121, 130405 (2018)
[3] R. Rossi, T. Ohgoe, E. Kozik, N. Prokof'ev, B. Svistunov, K. Van Houcke, F. Werner, "Contact and momentum distribution of the unitary Fermi gas", Phys. Rev. Lett. 121, 130406 (2018)