We extend the self-consistent Green's functions formalism to take into account three-body interactions. We analyze the perturbative expansion in terms of Feynman diagrams and define effective one- and two-body interactions, which allows for a substantial reduction of the number of diagrams. The procedure can be taken as a generalization of the normal ordering of the Hamiltonian to fully correlated density matrices. We give examples up to third order in perturbation theory. To define nonperturbative approximations, we extend the equation-of-motion method in the presence of three-body interactions. We propose schemes that can provide nonperturbative resummation of three-body interactions. We also discuss two different extensions of the Koltun sum rule to compute the ground state of a many-body system.

Neutron matter is an ideal laboratory for nuclear interactions derived from chiral effective field theory since all contributions are predicted up to next-to-next-to-next-to-leading order (${\mathrm{N}}^3\mathrm{LO}$) in the chiral expansion. By making use of recent advances in the partial-wave decomposition of three-nucleon ($3N$) forces, we include for the first time ${\mathrm{N}}^3\mathrm{LO} 3N$ interactions in many-body perturbation theory (MBPT) up to third order and in self-consistent Green's function theory (SCGF). Using these two complementary many-body frameworks we provide improved predictions for the equation of state of neutron matter at zero temperature and also analyze systematically the many-body convergence for different chiral EFT interactions. Furthermore, we present an extension of the normal-ordering framework to finite temperatures. These developments open the way to improved calculations of neutron-rich matter including estimates of theoretical uncertainties for astrophysical applications.

We present calculations for symmetric nuclear matter using chiral nuclear interactions within the self-consistent Green's functions approach in the ladder approximation. Three-body forces are included via effective one-body and two-body interactions, computed from an uncorrelated average over a third particle. We discuss the effect of the three-body forces on the total energy, computed with an extended Galitskii-Migdal-Koltun sum-rule, as well as on single-particle properties. Saturation properties are substantially improved when three-body forces are included, but there is still some underlying dependence on the similarity renormalization group evolution scale.

The properties of symmetric nuclear and pure neutron matter are investigated within an extended self-consistent Green's function method that includes the effects of three-body forces. We use the ladder approximation for the study of infinite nuclear matter and incorporate the three-body interaction by means of a density-dependent two-body force. This force is obtained via a correlated average over the third particle, with an in-medium propagator consistent with the many-body calculation we perform. We analyze different prescriptions in the construction of the average and conclude that correlations provide small modifications at the level of the density-dependent force. Microscopic as well as bulk properties are studied, focusing on the changes introduced by the density-dependent two-body force. The total energy of the system is obtained by means of a modified Galitskii-Migdal-Koltun sum rule. Our results validate previously used uncorrelated averages and extend the availability of chirally motivated forces to a larger density regime.

We exploit the many-body self-consistent Green's function method to analyze finite-temperature properties of infinite nuclear matter and to explore the behavior of the thermal index used to simulate thermal effects in equations of state for astrophysical applications. We show how the thermal index is both density and temperature dependent, unlike often considered, and we provide an error estimate based on our ab initio calculations. The inclusion of three-body forces is found to be critical for the density dependence of the thermal index. We also compare our results to a parametrization in terms of the density dependence of the nucleon effective mass. Our findings point to possible shortcomings of predictions made for the gravitational-wave signal from neutron-star merger simulations with a constant thermal index.

Pairing gaps in neutron matter need to be computed in a wide range of densities to address open questions in neutron-star phenomenology. Traditionally, the Bardeen-Cooper-Schrieffer approach has been used to compute gaps from bare nucleon-nucleon interactions. Here we incorporate the influence of short- and long-range correlations in the pairing gaps. Short-range correlations are treated, including the appropriate fragmentation of single-particle states, and substantially suppress the gaps. Long-range correlations dress the pairing interaction via density and spin modes and provide a relatively small correction. We use different interactions, some with three-body forces, as a starting point to control for any systematic effects. Results are relevant for neutron-star cooling scenarios, in particular in view of the recent observational data on Cassiopeia A.