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

TL;DR

This paper introduces a universal combinatorial framework for summing Feynman diagrams efficiently, enabling accurate calculations of the 2D SU(N) Hubbard model's equation of state in regimes difficult for existing methods.

Contribution

It presents a novel combinatorial and dynamic programming approach for summing Feynman diagrams, applicable to quantum many-body systems, with potential advantages on classical and quantum computers.

Findings

Successfully applied to 2D SU(N) Hubbard model

Achieved unbiased equation of state calculations

Demonstrated potential for quantum computational efficiency

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.