Auxiliary-Field Quantum Monte Carlo Simulations of Neutron Matter in Chiral Effective Field Theory

We present variational Monte Carlo calculations of the neutron matter equation of state using chiral nuclear forces. The ground-state wave function of neutron matter, containing nonperturbative many-body correlations, is obtained from auxiliary-field quantum Monte Carlo simulations of up to about 340 neutrons interacting on a $10^3$ discretized lattice. The evolution Hamiltonian is chosen to be attractive and spin independent in order to avoid the fermion sign problem and is constructed to best reproduce broad features of the chiral nuclear force. This is facilitated by choosing a lattice spacing of 1.5 fm, corresponding to a momentum-space cutoff of $\mathrm{\Lambda }=414\mathrm{MeV}/c$, a resolution scale at which strongly repulsive features of nuclear two-body forces are suppressed. Differences between the evolution potential and the full chiral nuclear interaction (Entem and Machleidt $\mathrm{\Lambda }=414\mathrm{MeV}$ [L. Coraggio et al., Phys. Rev. C 87, 014322 (2013)]) are then treated perturbatively. Our results for the equation of state are compared to previous quantum Monte Carlo simulations that employed chiral two-body forces at next-to-next-to-leading order (N2LO). In addition, we include the effects of three-body forces at N2LO, which provide important repulsion at densities higher than $0.02{\mathrm{fm}}^{-3}$ as well as two-body forces at next-to-next-to-next-to-leading order.

Figure 1

Momentum-space evolution potentials [see Eq. (4)] employed in the imaginary-time propagation of the trial wave function, corresponding to different densities. In the inset is shown the expectation values of the evolution potential (red solid circles) and the two-body chiral potential (blue squares) computed for the density $n=0.011{\mathrm{fm}}^{-3}$.

Figure 2

Occupation probabilities of neutron matter as a function of momentum for selected densities.

Figure 3

Equation of state of pure neutron matter calculated using AFQMC with the N3LO chiral two-nucleon potential (red circles) plus the N2LO three-nucleon contribution (blue diamonds). For comparison, we show the results of Gezerlis et al. [18], Roggero et al. [19], and Gezerlis and Carlson [44] of QMC calculations with two-body forces alone. In the upper inset, we show the contributions to the energy per particle from different orders in the chiral expansion (“$+$” and “$-$” refer to repulsive and attractive components, respectively). The lower inset demonstrates that the last term in Eq. (3) is perturbative.