Ab initio Green's functions approach for homogeneous nuclear matter

Homogeneous nuclear matter is investigated using the \textit{ab initio} Self-consistent Green’s function (SCGF) approach with nuclear interactions based on chiral effective field theory. The employed method, which combines the state-of-the-art algebraic diagrammatic construction approximation at third order with Gorkov correlations, is capable of computing both the equation of state (EOS) and single-particle properties of nuclear matter. The EOS calculated with our approach and coupled-cluster theory are shown to agree very well. The one-nucleon spectral functions and the momentum distributions are discussed to gain insights into the dynamics of the interacting nuclear matter.

💡 Research Summary

The paper presents a state‑of‑the‑art ab initio treatment of infinite homogeneous nuclear matter by combining the Self‑Consistent Green’s Function (SCGF) method with the Algebraic Diagrammatic Construction at third order (ADC(3)) and Gorkov‑type pairing correlations. The nuclear interaction employed is the chiral effective field theory (χEFT) Δ‑NNLO_go(450) potential, which includes two‑ and three‑nucleon forces with explicit Δ‑isobar contributions.

In the SCGF framework the central quantity is the one‑body Green’s function g₁₁(ω), obtained by solving the Dyson or Gorkov equation. The normal self‑energy Σ₁₁(ω) is approximated with the ADC(3) scheme, which respects the exact analytic structure of the self‑energy and implicitly sums perturbative contributions to all orders. Pairing correlations are incorporated through the anomalous self‑energy Σ₁₂(∞), treated at first order. To improve the description of higher‑order correlations, the authors also use the ADC(3)‑D variant, in which coupled‑cluster (CC) amplitudes from a preliminary CCD calculation are inserted into the ADC coupling matrices. This hybridization allows a direct comparison with standard CC calculations performed at the CCD(T) level (CCD plus perturbative triples).

Numerical calculations are carried out for symmetric nuclear matter (SNM) with 132 nucleons and pure neutron matter (PNM) with 66 neutrons, confined in a cubic box with periodic boundary conditions (PBC). For single‑particle observables, twist‑averaged boundary conditions (TABC) are employed to obtain a denser momentum mesh and reduce finite‑size effects. The equation of state (EOS) is evaluated as a function of density for both SNM and PNM. Results from ADC(3), ADC(3)‑D, and CCD(T) are virtually indistinguishable; the correlation energy per particle differs by less than 0.1 MeV across the three methods, demonstrating that both SCGF and CC capture the essential many‑body physics at the same level of accuracy.

The one‑nucleon spectral function S₁₁(k, ω) is presented as a two‑dimensional map of momentum k versus energy ω. In SNM, strong fragmentation appears for k > 1 fm⁻¹, with many satellite peaks reflecting intense correlations. In contrast, PNM shows a dominant quasiparticle peak with a much weaker background, consistent with the softer interaction in pure neutron matter. Near the Fermi momentum k_F, the spectral strength is concentrated in a single pole with occupation amplitudes V²≈1 for k < k_F and U²≈1 for k > k_F, confirming the Landau quasiparticle picture.

Momentum distributions ρ(k) reveal partial depletion of hole states (k < k_F) and a high‑momentum tail (k > k_F) generated by short‑range correlations. The depletion is substantially larger in SNM than in PNM, reflecting the stronger tensor and spin‑isospin components in the symmetric system. Both PBC and TABC results preserve the discontinuity at k_F, while TABC yields a smoother curve due to the finer k‑grid.

The authors conclude that the ADC‑SCGF approach provides a reliable, fully microscopic description of infinite nuclear matter, with results benchmarked against coupled‑cluster theory. The method is ready for extensions to superfluid neutron matter, the calculation of quasiparticle effective masses and lifetimes, and systematic studies across density and isospin asymmetry. Future work will also explore the impact of three‑body forces and higher‑order ADC truncations on the EOS and spectral properties, aiming at tighter constraints for astrophysical applications such as neutron‑star modeling.