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Contributions to unbiased diagrammatic methods for interacting fermions

Abstract : This thesis contributes to the development of unbiased diagrammatic approaches to the quan- tum many-body problem, which consist in computing expansions in Feynman diagrams to arbitrary order with no small parameter. The standard form of fermionic sign problem - expo- nential increase of statistical error with volume - does not affect these methods as they work directly in the thermodynamic limit. Therefore they are a powerful tool for the simulation of quantum matter. Part I of the thesis is devoted to the unitary Fermi gas, a model of strongly-correlated fermions accurately realized in cold-atom experiments. We show that physical quantities can be retrieved from the divergent diagrammatic series by a specifically-designed conformal-Borel transformation. Our results, which are in good agreement with experiments, demonstrate that a diagrammatic series can be summed reliably for a fermionic theory with no small parameter. In Part II we present a new efficient algorithm to compute diagrammatic expansions to high order. All connected Feynman diagrams are summed at given order in a computational time much smaller than the number of diagrams. Using this technique one can simulate fermions on an infinite lattice in polynomial time. As a proof-of-concept, we apply it to the weak-coupling Hubbard model, obtaining results with record accuracy. Finally, in Part III we address the problem of the misleading convergence of dressed dia- grammatic schemes, which is related to a branching of the Luttinger-Ward functional. After studying a toy model, we show that misleading convergence can be ruled out for a large class of diagrammatic schemes, and even for the fully-dressed scheme under certain conditions.
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Contributor : Riccardo Rossi <>
Submitted on : Thursday, February 8, 2018 - 4:27:31 PM
Last modification on : Tuesday, September 22, 2020 - 3:49:39 AM
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  • HAL Id : tel-01704724, version 1

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Riccardo Rossi. Contributions to unbiased diagrammatic methods for interacting fermions. Strongly Correlated Electrons [cond-mat.str-el]. Ecole Normale Supérieure (ENS), 2017. English. ⟨tel-01704724⟩

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