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

R. Rossi, T. Ohgoe, K. Van Houcke, and F. Werner

We consider 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 [1,2]. The diagrammatic series is divergent and there is no small parameter so that a resummation method is needed. Previously we used Abelian resummation methods, which are applicable under the assumption that the diagrammatic series has a non-zero radius of convergence; this led to good agreement with experimental data for the equation of state [2]. In our more recent work [3] we compute the large-order asymptotics of the diagrammatic series, based on a functional integral representation of the skeleton series [4] and the saddle-point method. We find 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. This yields new high-precision data, not only for the equation of state, but also for Tan’s contact coefficient – which depends only weakly on temperature due to two competing effects, and for the momentum distribution – which does not follow Fermi liquid theory [5].

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] K. Van Houcke, F. Werner, E. Kozik, N. Prokof’ev, B. Svistunov, M. Ku, A. Sommer, L. Cheuk, A. Schirotzek, M. Zwierlein, “Feynman diagrams versus Fermi-gas Feynman emulator”, Nature Phys. 8, 366 (2012)
[3] 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)
[4] R. Rossi, F. Werner, N. Prokof’ev, B. Svistunov, “Shifted-action expansion and applicability of dressed diagrammatic schemes”, Phys. Rev. B 93, 161102(R) (2016)
[5] 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)