$ extit{Ab initio}$ Exact Calculation of Strongly-Correlated Nucleonic Matter

Dense nucleonic matter is of vital importance for understanding compact stars and inferring the transition into deconfined quark phase. We present $\textit{ab initio}$ exact calculations of infinite nucleonic matter with the state-of-the-art full configuration-interaction quantum Monte Carlo (FCIQMC) method, enabling us to rigorously benchmark many-body methods and assess the degree to which the nucleonic matter is correlated. This method has been numerically validated by exact diagonalization within a small model space. Calculations of nucleonic matter using chiral nuclear forces reveal that symmetric nuclear matter is strikingly strongly correlated, raising questions on previous $\textit{ab initio}$ calculations of nuclear matter with many-body expansion truncations and offering insights into simultaneous descriptions of finite nuclei and infinite nucleonic matter from first principles.

💡 Research Summary

The authors present a groundbreaking “ab initio” study of infinite nuclear matter using the full configuration‑interaction quantum Monte Carlo (FCIQMC) method, a stochastic projector technique originally developed for quantum chemistry. FCIQMC represents the many‑body wave function as a population of signed walkers distributed over the complete set of Slater determinants. Walkers undergo spawning, death/cloning, and annihilation steps that together solve the imaginary‑time Schrödinger equation while mitigating the fermion sign problem. An initiator approximation and adaptive shift scheme allow systematic convergence toward the exact full‑CI limit as the total walker number increases.

The paper first validates the implementation on the exactly solvable Richardson pairing model (four nucleons in four levels). With ~10⁴ walkers, FCIQMC reproduces the exact diagonalization energies across weak to strong pairing strengths, whereas perturbative many‑body approaches (MBPT up to fourth order) and non‑perturbative methods (CCD, ADC(3)‑D, IMSRG(2)) deviate markedly once the interaction strength exceeds |g|≈1.0. This benchmark confirms that FCIQMC can capture all orders of correlation without bias.

Armed with this confidence, the authors turn to realistic infinite nuclear matter. They employ chiral effective‑field‑theory (χEFT) interactions at next‑to‑next‑to‑leading order (N²LO) in two variants: a Δ‑full N²LO GO potential (including the Δ(1232) isobar) and a Δ‑less N²LO potential with a 450 MeV cutoff. Both two‑ and three‑nucleon forces are included, the latter at the normal‑ordered two‑body level (though FCIQMC can treat the full three‑body term). The many‑body basis consists of Slater determinants built from plane‑wave single‑particle states in a cubic box with periodic boundary conditions; momentum cutoffs are chosen large enough to ensure convergence.

In a small model space (4 nucleons, 28 single‑particle states) the authors benchmark symmetric nuclear matter (SNM) against exact diagonalization. Across three densities (ρ=0.06, 0.16, 0.26 fm⁻³) FCIQMC energies differ from the exact solution by less than 10⁻⁴ MeV, while MBPT(2), MBPT(3) and IMSRG(2) show deviations that grow with density and are especially pronounced for the harder Δ‑full interaction. This illustrates that SNM is strongly correlated and that low‑order truncations miss substantial physics.

Large‑scale calculations are then performed for pure neutron matter (PNM) and SNM with up to 76 nucleons and over a thousand single‑particle states. For PNM, all methods (MBPT(2), MBPT(3), CCD, ADC(3)‑D, IMSRG(2), and FCIQMC) agree within 0.5 MeV per particle, reflecting the relatively weak correlations in neutron matter. In contrast, SNM exhibits systematic differences: FCIQMC yields the lowest binding energies, with other methods overbinding by up to ~2 MeV at saturation density and even larger discrepancies at higher densities. The Δ‑full interaction leads to a saturation point that is too dense and too bound for all methods, but the magnitude of the error is smallest for FCIQMC, indicating that missing high‑order correlations account for roughly 10 MeV of the binding energy at ρ₀ and up to 40 MeV at 2 ρ₀.

When the Δ‑less N²LO potential is used, the situation changes. Earlier Brueckner‑Hartree‑Fock studies claimed that this interaction fails to saturate SNM. The present work shows that the failure is largely a consequence of the many‑body truncations employed; FCIQMC again predicts the lowest energies, while MBPT(3) and ADC(3)‑D remain close, and MBPT(2) deviates dramatically, indicating poor convergence. IMSRG(2) accidentally reproduces the empirical saturation point, but this appears to be a fortuitous cancellation rather than a reliable prediction.

Overall, the study demonstrates that FCIQMC provides an essentially exact benchmark for infinite nuclear matter, quantifying the importance of high‑order many‑body correlations that are omitted in commonly used expansion‑truncated approaches. The results have immediate implications for the nuclear equation of state, the symmetry energy, and astrophysical modeling of neutron stars, as well as for the development of more accurate, systematically improvable many‑body methods in nuclear theory.