# Summation of diagrammatic series for a strongly correlated fermionic theory with zero convergence radius

Felix Werner, Department of Physics, ENS Paris

10.11.2017 at 09:00

For fermionic lattice-models, diagrammatic series typically converge in some region of the phase

diagram, which allowed to obtain a series of new results using diagrammatic Monte Carlo in the

last 10 years. I will present our work on a continuous -space model, the unitary Fermi gas, a

textbook model most relevant to ultracold atoms. We find that even though the diagrammatic

series have zero convergence radius, it is possible to obtain convergence towards the exact

result, thanks to a conformal-Borel transformation that takes into account the large-order

behavior and the analytic structure standing behind the series [1]. The starting point of our

analysis is to construct an action that generates a dressed diagrammatic series [2], as I will

explain for the Hubbard model in the first part of the talk.

[1] R. Rossi, T. Ohgoe, K. Van Houcke, F. Werner, in preparation.

[2] R. Rossi, F. Werner, N. Prokof'ev, B. Svistunov, PRB 93, 161102 (2016).

A 450, Theresienstr. 37