Quantum Monte Carlo formalism for dynamical pions and nucleons

Abstract

In most simulations of nonrelativistic nuclear systems, the wave functions found solving the many-body Schrödinger equations describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. In this work we present an alternative quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. We report the renormalization of the nucleon mass as a function of the momentum cutoff, an Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two-nucleon sector we show that the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and we fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. We show that the method can be readily applied to light-nuclei.

17 pages, 10 figures

References in corpus (8)

• Chiral effective field theory and nuclear forces
• Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory
• Local chiral effective field theory interactions and quantum Monte Carlo applications
• Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order
• Ground-State Properties of ${}^4$He and ${}^{16}$O Extrapolated from Lattice QCD with Pionless EFT
• Quantum Monte Carlo calculations of light nuclei with local chiral two- and three-nucleon interactions
• Volume Dependence of N-Body Bound States
• Analyzing the Fierz Rearrangement Freedom for Local Chiral Two-Nucleon Potentials

Cited by in corpus (7)

• Nuclear effective field theory: status and perspectives
• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Quantum Monte Carlo Methods in Nuclear Physics: Recent Advances
• Neutrino-nucleus cross section within the extended factorization scheme
• Electron scattering on $\mathbf{A}=3$ nuclei from quantum Monte Carlo based approaches
• Electroweak pion-production on nuclei within the extended factorization scheme
• Cold atoms beyond atomic physics