Resummation of diagrammatic series with zero convergence radius for the unitary Fermi gas
Feynman diagrams are powerful tools for studying various fields of physics. Still, the analysis usually involves approximations, because only some types of diagrams or low-order diagrams are considered there. However, the Monte Carlo method for unbiased sampling of Feynman diagrams has been recently developed. On the other hand, the diagrammatic series sometimes have zero radius of convergence. The question is whether it is still possible to make accurate predictions by summing up Feynman diagrams.
In this talk, we report high-precision results obtained by the bold-line diagrammatic Monte Carlo method for the unitary Fermi gas with zero convergence radius. We derive the large-order asymptotic behavior of the diagrammatic series, and we give mathematical arguments and numerical evidence for the resummability of the series by a specifically designed conformal-Borel transformation that incorporates the large-order behavior. Combining this new resummation method with diagrammatic Monte Carlo evaluation up to order 9, we obtain new results for the equation of state, which agree with the ultracold-atom experimental data, except for the 4-th virial coefficient for which our data point to the theoretically conjectured value.
R.Rossi, T. Ohgoe, K. Van Houcke, and F. Werner, arXiv:1802.07717