Diagrammatic ab initio methods for infinite nuclear matter with modern chiral interactions

A comparative study of the equation of state for pure neutron matter and symmetric nuclear matter is presented using three ab initio methods based on diagrammatic expansions: coupled-cluster theory, self-consistent Green’s functions, and many-body perturbation theory. We critically evaluate these methods by employing different chiral potentials at next-to-next-to-leading-order – all of which include both two- and three-nucleon contributions – and by exploring various many-body truncations. Our investigation yields highly precise results for pure neutron matter and robust predictions for symmetric nuclear matter, particularly with soft interactions. Moreover, the new calculations demonstrate that the $\rm{ NNLO_{sat} }(450)$ and $Δ\rm{NNLO_{go}}(394)$ potentials are consistent with the empirical constraints on the saturation point of symmetric nuclear matter. Additionally, this benchmark study reveals that diagrammatic expansions with similar architectures lead to consistent many-body correlations, even when applied across different methods. This consistency underscores the robustness of the diagrammatic approach in capturing the essential physics of nucleonic systems.

💡 Research Summary

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This paper presents a comprehensive benchmark of three diagrammatic ab initio many‑body methods—coupled‑cluster theory (CC), self‑consistent Green’s functions (SCGF), and third‑order many‑body perturbation theory (MBPT(3))—applied to infinite nuclear matter. The authors focus on two key systems: pure neutron matter (PNM) and symmetric nuclear matter (SNM) at zero temperature, and they employ modern chiral effective‑field‑theory (χEFT) interactions at next‑to‑next‑to‑leading order (NNLO) that contain both two‑nucleon (NN) and three‑nucleon (3N) forces. Three representative potentials are used: NNLO_sat(450), ΔNNLO(450), and ΔNNLO_go(394), all regularized with non‑local cutoffs.

The many‑body calculations are performed in a finite‑size box with periodic boundary conditions. “Magic” particle numbers (66 neutrons for PNM, 132 nucleons for SNM) are chosen to minimize finite‑size effects. Momentum space is truncated either spherically (N_max² = 25) for SCGF and MBPT or cubically (|n_i| ≤ 4) for CC, and convergence with respect to the model‑space size is explicitly verified.

In the CC sector, the authors solve the CCD equations (doubles only) and add perturbative triples via the CCD(T) correction. This yields an energy that is exact through fourth order in MBPT and is widely regarded as a “gold standard” for ground‑state energies. The SCGF implementation uses the Dyson‑ADC(3) scheme, which resums infinite ladder and ring diagrams while treating the dynamical self‑energy with a frequency‑dependent part built from an optimized reference state (OpRS). An extended version, ADC(3)‑D, incorporates the converged CC T₂ amplitudes to generate additional diagram classes. MBPT(3) is carried out in the same finite‑volume discretization as the other methods, with the normal‑ordered two‑body (NO2B) approximation used for the three‑body contributions at third order.

Numerical results show remarkable agreement among the three approaches for PNM across densities up to about twice saturation (ρ ≈ 0.3 fm⁻³). The spread in energy per particle is typically ≤ 0.5 MeV, well within the intrinsic uncertainty of the chiral interactions themselves. For SNM, the agreement remains excellent when soft interactions (NNLO_sat, ΔNNLO_go) are used; CC and SCGF differ by less than 1 MeV, and MBPT(3) stays within 1–2 MeV. With harder cutoffs, CC and SCGF predict slightly larger correlation energies than MBPT(3), indicating slower perturbative convergence.

A key finding is that both NNLO_sat(450) and ΔNNLO_go(394) reproduce the empirical saturation point of symmetric nuclear matter (ρ₀ ≈ 0.16 fm⁻³, E/A ≈ –16 MeV) within the calculated uncertainties. This demonstrates that modern NNLO χEFT potentials, when combined with a consistent treatment of 3N forces, can simultaneously describe finite nuclei and bulk nuclear matter.

The authors also analyze the computational scaling of each method. CCD(T) scales as O(N⁶) and is the most demanding in memory but provides the highest accuracy. ADC‑SCGF scales as O(N⁵); the most expensive step is the evaluation of the dynamical self‑energy, yet the method yields single‑particle observables (momentum distributions, spectral functions) alongside the total energy. MBPT(3) scales as O(N⁴) and is computationally cheap, making it attractive for large‑scale surveys, but its reliability diminishes for stiff interactions.

Overall, the study confirms that diagrammatic expansions with similar topologies generate consistent many‑body correlations across different many‑body frameworks. This robustness supports the use of such diagrammatic ab initio methods as reliable tools for nuclear‑matter physics, and it provides a clear roadmap for future extensions: inclusion of higher‑order χEFT forces (N³LO, N⁴LO), explicit four‑nucleon forces, finite‑temperature extensions, and applications to asymmetric matter relevant for neutron‑star crusts. The benchmark also offers practical guidance on the trade‑off between computational cost and accuracy, which will be valuable for the next generation of large‑scale nuclear‑theory calculations.