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

Abstract

Dense nucleonic matter is of vital importance for understanding compact stars and inferring the transition into deconfined quark phase. We present the $\textit{ab initio}$ 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 the 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.

Figures (4)

• Figure 1: Benchmark results for the Richardson model with $\delta=1.0$. (a) and (b) show the correlation energies as functions of the pairing strength $g$. (c) and (d) display the deviations of various many-body methods with respect to the exact solution.
• Figure 2: Comparison of many-body methods for SNM in a small model space (4 nucleons, 28 single-particle basis states), benchmarked against exact results at three densities. The bars represent the absolute errors in the ground-state energy for MBPT(2), MBPT(3), IMSRG(2), and FCIQMC. Note that the FCIQMC errors have been magnified by a factor of 100 for visualization, with their statistical uncertainty also shown. Calculations were performed using both $\Delta$-less [$\mathrm{N^\nu LO\; EMN(\Lambda)}$] PhysRevC.96.024004 and $\Delta$-full [$\mathrm{\Delta N^\nu LO(\Lambda)}$] PhysRevC.97.024332PhysRevC.102.054301 interactions, in which $\nu$ denotes the chiral order and $\Lambda$ is the cutoff (in MeV).
• Figure 3: Energies per particle of PNM, SNM, and the nuclear symmetry energy $S(\rho)$ per nucleon as functions of density $\rho$. Calculations use the $\Delta$-full $\mathrm{\Delta N^2LO_{GO}}$ interaction. The FCIQMC results are compared with MBPT(2), MBPT(3), ADC(3)-D, CCD and IMSRG(2) in the same model space. The Hartree-Fock solutions are marked by dash-dot curves. The empirical saturation density is marked by vertical gray lines. Bottom panels show the energy differences of other methods relative to our FCIQMC results, highlighting the contribution of neglected correlations.
• Figure 4: Same as Fig. \ref{['fig:eos_go']} but for calculations using the $\Delta$-less $\mathrm{N^2LO}$ interaction with cutoff 450 MeV from Hüther et alHUTHER2020135651. The discrepancies between FCIQMC and other truncated methods are much more evident for SNM.