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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).

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