Symmetry-Projected Hartree-Fock-Bogoliubov Emulation

Abstract

Nuclear systems consist of strongly interacting protons and neutrons. The general structure of these many-body systems can often be described by the nuclear shell model. The shell model predicts that there are certain nucleon numbers, referred to as magic numbers, which result in particularly stable configurations. These configurations are well described by spherical mean-field methods such as Hartree- Fock. Nuclei that are singly or doubly non-magic may, however, exhibit emergent deformations or pairing correlations, making the typical spherical mean-field approach insufficient. Deformations are conveniently captured by allowing the mean-field solutions to break rotational and/or parity symmetries. Pairing correlations are incorporated with the Hartree-Fock-Bogoliubov method, which employs Bogoliubov quasiparticles that potentially break particle number conservation. The broken symmetries must be restored to obtain physical states with good quantum numbers and to accurately calculate certain observables. Contemporary models of the nuclear Hamiltonian are based on chiral effective field theory and involve free parameters referred to as low-energy constants. Exploring the continuous parameter space of these interaction models becomes computationally expensive with Hartree-Fock or Hartree-Fock-Bogoliubov solvers. The purpose of this project is to develop Eigenvector Continuation emulators for symmetrybreaking and symmetry-restored states, to approximate ground-state energies at a significantly reduced computational cost. In this work we vary only the C1S0 low-energy constant, and thus explore a one-dimensional parameter space. We find that our emulators perform well using only three to six training points. For example, interpolation of the 18O ground-state energy with restored particle number gives ∼ 0.7 MeV error on average within an output energy range of approximately 400 MeV. Emulators constructed from states with broken angular momentum (without restoration) perform similarly, giving ∼ 0.7 MeV errors on average. In conclusion, emulators can accurately reproduce Hartree-Fock-Bogoliubov ground-state energies before and after symmetry restoration with errors on the order of 1 MeV for nuclear systems with mass number ≈ 20.