We present the first quantum Monte Carlo (QMC) calculations with chiral effective field theory (EFT) interactions. To achieve this, we remove all sources of nonlocality, which hamper the inclusion in QMC calculations, in nuclear forces to next-to-next-to-leading order. We perform auxiliary-field diffusion Monte Carlo (AFDMC) calculations for the neutron matter energy up to saturation density based on local leading-order, next-to-leading order, and next-to-next-to-leading order nucleon-nucleon interactions. Our results exhibit a systematic order-by-order convergence in chiral EFT and provide nonperturbative benchmarks with theoretical uncertainties. For the softer interactions, perturbative calculations are in excellent agreement with the AFDMC results. This work paves the way for QMC calculations with systematic chiral EFT interactions for nuclei and nuclear matter, for testing the perturbativeness of different orders, and allows for matching to lattice QCD results by varying the pion mass.

We present quantum Monte Carlo calculations of light nuclei, neutron-α scattering, and neutron matter using local two-and three-nucleon (3N) interactions derived from chiral effective field theory up to next-to-next-to-leading order (N 2 LO). The two undetermined 3N low-energy couplings are fit to the 4 He binding energy and, for the first time, to the spin-orbit splitting in the neutron-α P -wave phase shifts. Furthermore, we investigate different choices of local 3N-operator structures and find that chiral interactions at N 2 LO are able to simultaneously reproduce the properties of A = 3, 4, 5 systems and of neutron matter, in contrast to commonly used phenomenological 3N interactions.Three-nucleon (3N) interactions are essential for a reliable prediction of the properties of light nuclei and nucleonic matter [1][2][3][4][5]. In quantum Monte Carlo (QMC) calculations phenomenological 3N interactions such as the Urbana [6] and Illinois [7] models have been used with great success [3,8]. However, such models suffer from certain disadvantages: They are not based on a systematic expansion and it was found that the Illinois forces tend to overbind neutron matter [9,10]. It is therefore unlikely that these phenomenological models can be used to correctly predict the properties of heavy neutron-rich nuclei.An approach which addresses these shortcomings is chiral effective field theory (EFT) [2,[11][12][13][14]. Chiral EFT is a low-energy effective theory consistent with the symmetries of quantum chromodynamics and provides a systematic expansion for nuclear forces. It includes contributions from long-range pion-exchange interactions explicitly and expands the short-distance interactions into a systematic set of contact operators accompanied by low-energy couplings fit to experimental data. Chiral EFT enables the determination of theoretical uncertainties and systematic order-by-order improvement; for recent work see Refs. [15][16][17][18].Chiral EFT also predicts consistent many-body interactions. In Weinberg power counting, 3N forces first enter at next-to-next-to-leading order (N 2 LO) [19,20] and contain three contributions: A two-pion-exchange interaction V C , a one-pion-exchange-contact interaction V D , and a 3N contact interaction V E . While the first is accompanied by the couplings c i from the pion-nucleon sector, the latter two are accompanied by the couplings c D and c E , which have to be determined in A > 2 systems.In addition to systematic nuclear forces, reliable manybody methods are required to describe properties of light nuclei and of dense neutron matter. QMC approaches, which solve the many-body Schrödinger equation stochastically, are such a class of methods. Both the Green's function Monte Carlo (GFMC) method and the auxiliary-field diffusion Monte Carlo (AFDMC) method rely on projection in imaginary time τ ,with H the Hamiltonian of the system and |Ψ T a trial wave function not orthogonal to the many-body ground state |Ψ 0 . For a recent review of developments and applications of QMC methods...

The properties of low-density neutron matter are important for the understanding of neutron star crusts and the exterior of large neutron-rich nuclei. We examine various properties of dilute neutron matter using quantum Monte Carlo methods, with s- and p-wave terms in the interaction. Our results provide a smooth evolution of the equation of state and pairing gap from extremely small densities, where analytic expressions are available, up to the strongly interacting regime probed experimentally and described theoretically in cold atomic systems, where the Fermi momentum is approximately half an inverse fermi and the pairing gap becomes of the order of magnitude of the Fermi energy. We also present results for the momentum distribution and pair distributions, displaying the same evolution from weak to strong coupling. Combined with previous quantum Monte Carlo and other calculations at moderate densities, these results provide strong constraints on the neutron matter equation of state up to saturation densities.Comment: 10 pages, 9 figures; 2 references added; v2 corresponds to the published versio