Multi-strangeness matter from ab initio calculations

TL;DR

This work develops an ab initio, sign-problem free framework that unifies hypernuclear structure and dense hypernuclear matter by integrating Nuclear Lattice Effective Field Theory with a novel AFQMC algorithm. It includes full two- and three-body hyperon-nucleon and hyperon-hyperon interactions and constrains them with light hypernuclei data, enabling predictions from light to medium-mass hypernuclei and the equation of state of beta-stable matter. The results show a consistent onset of $\Lambda$ hyperons in dense matter and neutron stars with masses around $2\,M_\odot$, with tidal deformabilities matching gravitational-wave constraints, thus addressing the hyperon puzzle within a unified microscopic framework. The study demonstrates that hyperons can be accommodated in massive neutron stars without violating current astrophysical observations, establishing a direct link between hypernuclear structure, dense matter composition, and neutron-star phenomenology.

Abstract

Hypernuclei and hypernuclear matter connect nuclear structure in the strangeness sector with the astrophysics of neutron stars, where hyperons are expected to emerge at high densities and affect key astrophysical observables. We present the first {\em ab initio} calculations that simultaneously describe single- and double-$Λ$ hypernuclei from the light to medium-mass range, the equation of state for $β$-stable hypernuclear matter, and neutron star properties. Despite the formidable complexity of quantum Monte Carlo~(QMC) simulations with multiple baryonic degrees of freedom, by combining nuclear lattice effective field theory with a newly developed auxiliary-field QMC algorithm we achieve the first sign-problem free {\em ab initio} QMC simulations of hypernuclear systems containing an arbitrary number of neutrons, protons, and $Λ$ hyperons, including all relevant two- and three-body interactions. This eliminates reliance on the symmetry-energy approximation, long used to interpolate between symmetric nuclear matter and pure neutron matter. Our unified calculations reproduce hyperon separation energies, yield a neutron star maximum mass consistent with observations, predict tidal deformabilities compatible with gravitational-wave measurements, and give a trace anomaly in line with Bayesian constraints. By bridging the physics of finite hypernuclei and infinite hypernuclear matter within a single {\em ab initio} framework, this work establishes a direct microscopic link between hypernuclear structure, dense matter composition, and the astrophysical properties of neutron stars.

Figures (6)

• Figure 1: Single-$\Lambda$ separation energies and double-$\Lambda$ separation energies for hypernuclei. Hypernuclei used to fit the $NN\Lambda$ and $N\Lambda\Lambda$ forces are depicted by blue squares. Predictions are shown as red circles for single-$\Lambda$ hypernuclei up to $_\Lambda^{89}$Y and double-$\Lambda$ hypernuclei up to $_{\Lambda\Lambda}^{12}$Be. Error bars represent the combined statistical and systematic uncertainties. NLEFT results are compared with experimental data from the Hypernuclear Database (green) Eckert2023, and with recent ab initio predictions from the variational Monte Carlo method based on neural network quantum states (VMC-NQS, orange) DiDonna:2025oqf and the no-core shell model (NCSM, purple) Knoll:2023mqk.
• Figure 2: EoSs of $\beta$-stable nuclear matter (NM) and hypernuclear matter (HNM). The blue dashed line denotes the $\beta$-stable NM, obtained from the $NN$ and $NNN$ interactions. The red solid line represents the HNM EoS including hyperons interacting via two-body ($N\Lambda$, $\Lambda\Lambda$) and three-body forces ($NN\Lambda$, $N\Lambda\Lambda$). Open circle indicates the $\Lambda$ threshold densities, $\rho_\Lambda^{\rm th}$. The inset displays the corresponding speed of sound for NM and HNM. The orange shaded regions show the final posterior estimate for the neutron star EoS constrained by $\chi$EFT, pQCD, and astrophysical observations Koehn:2024set, while the green shaded regions represent the posterior estimate constrained by astronomical observations together with nuclear experimental data Tsang:2023vhh.
• Figure 3: Left Panel: Neutron star mass-radius relation. The legend is the same as of Fig. \ref{['fig2']}. The gray horizontal dotted line marks 2$M_\odot$. The inner and outer shaded contours indicate the mass-radius constraints from NICER’s analysis of PSR J0030+0451 Vinciguerra2024APJ, PSR J0740+6620 Salmi2024APJ, PSR J0437-4715 Choudhury2024APJ, and PSR J0614-3329 Mauviard:2025dmd. The inset shows the neutron star mass as a function of central density, together with the corresponding $\Lambda$-hyperon particle fractions. Right Panel: Neutron star tidal deformability $\Lambda$ as a function of mass.$\Lambda(M)$ is compared with the masses and tidal deformabilities inferred in Ref. Fasano:2019zwm for the two neutron stars in the merger event GW170817 (open squares) as well as $\Lambda(1.4M_\odot)$ extracted from GW170817 LIGOScientific:2018cki (open circle). The green dot-dashed line represents the pure neutron matter (PNM) from the previous NLEFT calculations Tong:2025sui. The gray star denotes the result from auxiliary-field diffusion Monte Carlo (AFDMC) using their parameterization (II) of the $NN\Lambda$ force. Lonardoni:2014bwa.
• Figure S1: 3D plot showing the energy for HNM. Energy per baryon $E_{\rm HNM}/N_{\rm tot}$ as a function of proton number $N_p$ and $\Lambda$ hyperon number $N_\Lambda$ at fixed density $\rho=0.6$ fm$^{-3}$. The green circle indicates the equilibrium composition of $\beta$-stable matter at this density. The color scale denotes the magnitude of the energy per baryon.
• Figure S2: Particle fractions in $\beta$-stable HNM. Density dependence of the particle fractions $x_i(\rho)$ for neutrons ($x_n$), protons ($x_p$), $\Lambda$ hyperons ($x_\Lambda$), electrons ($x_e$), and muons ($x_\mu$) are shown. Bands indicate statistical and systematic uncertainties of the NLEFT calculations.