Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime

Abstract

We develop a numerically exact method for the summation of irreducible Feynman diagrams for fermionic self-energy in the thermodynamic limit. The technique, based on the Diagrammatic Determinant Monte Carlo and its recent extension to connected diagrams, allows us to reach high ($\sim 10$) orders of the weak-coupling expansion for the self-energy of the two-dimensional Hubbard model. Access to high orders reveals a non-trivial analytic structure of the self-energy and enables its controlled reconstruction with arbitrary momentum resolution in the nonperturbative regime of essentially strong correlations, which has recently been reached with ultracold atoms in optical lattices.

5 pages, 4 figures, published version

References in corpus (7)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
• Emergent BCS regime of the two-dimensional fermionic Hubbard model: ground-state phase diagram
• Fast Summation of Divergent Series and Resurgent Transseries in Quantum Field Theories from Meijer-G Approximants
• Determinant Monte Carlo algorithms for dynamical quantities in fermionic systems
• Direct sampling of the self-energy with Connected Determinant Monte Carlo

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