Quantum Monte Carlo formalism for dynamical pions and nucleons

TL;DR

This paper introduces a quantum Monte Carlo approach that explicitly includes relativistic pions and nonrelativistic nucleons, providing new insights into nuclear interactions and enabling applications to light nuclei.

Contribution

It presents a novel formalism incorporating both pions and nucleons explicitly in quantum Monte Carlo simulations, advancing nuclear many-body theory.

Findings

Renormalization of nucleon mass with momentum cutoff

Pion cloud density and momentum distributions computed

Reproduction of deuteron binding energy and neutron interactions

Abstract

In most simulations of nonrelativistic nuclear systems, the wave functions found solving the many-body Schr\"odinger 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.