Quantum Monte Carlo Calculations with Chiral Effective Field Theory Interactions (1303.6243v2)

Abstract: 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.

Quantum Monte Carlo Calculations with Chiral Effective Field Theory Interactions

This paper details a pioneering paper whereby Quantum Monte Carlo (QMC) calculations were conducted using chiral effective field theory (EFT) interactions, overcoming significant challenges associated with nonlocal forces. The authors' research primarily addresses the incorporation of chiral EFT interactions into QMC methods by removing nonlocal components—specifically to next-to-next-to-leading order (N²LO)—allowing accurate computation of neutron matter energies up to saturation density.

Chiral EFT is a robust framework leveraging the symmetries of quantum chromodynamics to model strong interactions at low energies. Despite its advantages, the inclusion of these interactions in QMC calculations has been hampered by nonlocality in momentum space. The authors tackle this by reformulating interactions to be local, thus enabling the use of QMC methodologies without the simplifications typically required.

The paper employs auxiliary-field diffusion Monte Carlo (AFDMC) to compute neutron matter energy utilizing nucleon-nucleon (NN) interactions at distinct chiral orders—leading order (LO), next-to-leading order (NLO), and N²LO—demonstrating systematic convergence across these orders. Perturbative methods corroborate the fidelity of AFDMC results for softer interactions, while making the first significant case for the perturbative treatment of chiral EFT interactions corresponding to low momentum cutoffs.

Key Findings and Implications

1. Local Chiral EFT Potentials: The research introduces a framework for constructing local chiral EFT potentials by eliminating sources of nonlocality up to N²LO, thus making them suitable for application in QMC calculations.
2. Systematic Order-by-Order Convergence: The AFDMC results provide clear evidence of convergence in the neutron matter equation of state when moving from LO to N²LO interactions. For N²LO potentials, the results highlight the progress in achieving precision with constraints obtained by varying cutoff scales.
3. Benchmarking and Perturbative Validation: A novel nonperturbative benchmark for neutron matter at nuclear densities is established. The comparison between AFDMC results and perturbative calculations reveals compatibility, especially for softer interaction profiles, thereby validating the perturbative approach's viability under certain conditions.
4. Future Directions: The methodology sets a precedent for employing chiral EFT in constraining nuclear matter models and understanding dense matter astrophysics. Anticipated future work includes integrating local N²LO three-nucleon (3N) forces into QMC calculations, further extending the potential for accurate modeling of nuclear phenomena and improving the connection to first-principles calculations based on QCD.

Conclusion

This paper represents a critical advancement in applying chiral EFT interactions within QMC frameworks, offering a methodologically sound approach for nonlocal to local interaction conversion. The work not only enables more comprehensive simulation of nuclear matter properties but also reinforces the synergy between theoretical frameworks and numerical techniques in nuclear physics. Anticipated extensions of this framework could significantly advance our understanding of both finite nuclei and bulk nuclear matter, potentially impacting interpretations of experimental results in nuclear structure and reactions, as well as informing astrophysical models of neutron stars.