This paper presents an automated, GPU-accelerated framework that pushes many-body perturbation theory (MBPT) calculations of the zero-temperature nuclear equation of state (EOS) to fifth order. The authors combine automated diagram generation and automated evaluation to handle the rapid growth in the number of diagrams that appear at high MBPT orders. Using these tools, they evaluate all 840 fifth-order diagrams at the normal-ordered two-body level and control the numerical uncertainties in those calculations.

The team built on an automated diagram generator (ADG) and extended it to produce analytic MBPT expressions up to sixth order, then evaluated those expressions up to fifth order. Key technical advances include multi-GPU acceleration for the costly normal-ordering step that turns some three-nucleon (3N) forces into effective two-body forces, and a new Monte Carlo integrator called PVegas that uses importance sampling to evaluate high-dimensional integrals. The authors also explicitly include the remaining residual three-body contributions up to third order (15 diagrams) to test how important those neglected pieces are.

At a conceptual level, MBPT is a step-by-step expansion that adds corrections to a simple reference state to capture interactions among many nucleons. Three-nucleon forces are important in nuclear matter, so the authors use normal ordering to include the dominant parts of those forces as a density-dependent two-body potential, and they keep the smaller residual three-body diagrams explicitly up to third order. Automating the algebra and using GPUs and smarter Monte Carlo sampling lets them compute hundreds of high-order diagrams that would be impractical by hand.

The work matters because higher-order MBPT lets researchers study how the perturbation series behaves and where it becomes unreliable. The framework makes it possible to test MBPT convergence in pure neutron matter and symmetric nuclear matter, to study neutron-star matter, and to produce fourth-order results for asymmetric matter including normal-ordered 3N forces. Those results help benchmark MBPT against nonperturbative methods and can guide resummation techniques that try to extract stable answers from slowly converging series.