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arXiv · 2309.13774

Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model

Evgeny Kozik
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Abstract

Feynman's diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a universal framework for efficient summation of connected or skeleton Feynman diagrams for generic quantum many-body systems. It is based on an explicit combinatorial construction of the sum of the integrands by dynamic programming, at a computational cost that can be made only exponential in the diagram order on a classical computer and potentially polynomial on a quantum computer. We illustrate the technique by an unbiased diagrammatic Monte Carlo calculation of the equation of state of the $2D$ $SU(N)$ Hubbard model in an experimentally relevant regime, which has remained challenging for state-of-the-art numerical methods.

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Evgeny Kozik. 2023-09-24. Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model. https://doi.org/10.1038/s41467-024-52000-6

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