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Powerful and deceptive Feynman diagrammatic series

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Development of the diagrammatic Monte Carlo (DiagMC) technique has allowed summation of Feynman diagrammatic series to high order, potentially leading to unbiased results. I will discuss how DiagMC can be used to address the Hubbard model on the square lattice in the region of moderate on-site repulsion U -which expresses the thermodynamic grand potential in terms of the interacting single-particle Green’s function G--is at least double valued with a distinct unphysical branch. Although the skeleton (bold-line) series in terms of G is found to converge despite this pathology (at least at moderate temperatures), at stronger interactions its convergence is to the unphysical branch, which reveals a new scenario of breaking down of diagrammatic expansions.

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