Felix Werner (Laboratoire Kastler Brossel, ENS & Collège de France):

Large-order summation of connected Feynman diagrams for strongly correlated fermions

    

A major long-standing goal is to develop generic unbiased methods for many-fermion problems. Conventional Quantum Monte Carlo methods (e.g. auxiliary-field QMC or lattice QCD) generically suffer from the "fermion sign problem": The computational time increases exponentially with the number of fermions. In contrast, expansions of intensive quantities in series of connected Feynman diagrams can be computed directly in the thermodynamic limit. Over the last decade, diagrammatic Monte Carlo algorithms made it possible to reach large expansion orders, and to obtain state-of-the-art results for various models of interacting fermions in 2 and 3 dimensions. The "Connected Determinant" algorithm allows to sum a factorial number of connected diagrams in an exponential time [1], leading to a computational time that increases only polynomially with the precision [2]. The range of applicability of the approach can be considerably enlarged by two ingredients: divergent-series summation methods, and modification of the expansion by changing the starting point and/or using dressed propagators/vertices. An important aspect is to understand the singularities of the function that stands behind the series. I will present illustrative results for the unitary Fermi gas in the normal phase [3,4] and the superconducting phase of the polarized attractive Hubbard model [5]. 

 

[1] Rossi, PRL 119, 045701 (2017)

[2] Rossi, Prokof’ev, Svistunov, Van Houcke, FW, EPL 118, 10004 (2017)

[3] Rossi, Ohgoe, Van Houcke, FW, PRL 121, 130405 (2018)

[4] Rossi, Ohgoe, Kozik, Prokof’ev, Svistunov, Van Houcke, FW, PRL 121, 130406 (2018)

[5] Spada, Rossi, Simkovic, Garioud, Ferrero, Van Houcke, FW, arXiv:2103.12038