Ab initio calculation of hyper-neutron matter

Abstract: The equation of state (EoS) of neutron matter plays a decisive role in our understanding of the properties of neutron stars as well as the generation of gravitational waves in neutron star mergers. At sufficient densities, it is known that the appearance of hyperons generally softens the EoS, thus leading to a reduction in the maximum mass of neutron stars well below the observed values of about 2 solar masses. Even though repulsive three-body forces are known to solve this so-called "hyperon puzzle", so far performing \textit{ab initio} calculations with a substantial number of hyperons has remained elusive. In this work, we address this challenge by employing simulations based on Nuclear Lattice Effective Field Theory with up to 232 neutrons (pure neutron matter) and up to 116 $\Lambda$ hyperons (hyper-neutron matter) in a finite volume. We introduce a novel auxiliary field quantum Monte Carlo algorithm, allowing us to simulate for both pure neutron matter and hyper-neutron matter systems up to 5 times the density of nuclear matter using a single auxiliary field without any sign oscillations. Also, for the first time in {\em ab initio} calculations, we not only include $N\Lambda$ two-body and $NN\Lambda$ three-body forces, but also $\Lambda\Lambda$ and $N \Lambda\Lambda$ interactions. Consequently, we determine essential astrophysical quantities such as the mass-radius relation, the speed of sound and the tidal deformability of neutron stars. Our findings also confirm the existence of the $I$-Love-$Q$ relation, which gives access to the moment of inertia of the neutron star.