Ab initio Bogoliubov many-body perturbation theory: closed-form constraint on the average particle number

Abstract

Bogoliubov many-body perturbation theory (BMBPT) relying on the breaking of U(1) global gauge symmetry has been recently formulated and applied to extend the applicability of standard perturbation theory to ab initio calculations of atomic nuclei away from shell closures. So far, practical applications have been limited to second-order calculations due to the lack of a generic algorithm to constrain the average particle number of the symmetry-broken state. This limitation is presently lifted and a general BMBPT formalism is presented that allows to constrain the particle-number expectation value at arbitrary order P. The constraint can be incorporated in closed form by solving a polynomial equation of degree P-1. The numerical procedure is illustrated through BMBPT(3) calculations of calcium isotopes using a nuclear Hamiltonian derived within chiral effective field theory.

arXiv commentaccepted version, 9 pages, 5 figures

References in corpus (35)

• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• Improved nuclear matter calculations from chiral low-momentum interactions
• Nuclear effective field theory: status and perspectives
• Chiral three-nucleon forces and neutron matter
• Three-body forces: From cold atoms to nuclei
• Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation
• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Ab initio predictions link the neutron skin of ${}^{208}$Pb to nuclear forces
• Non-Empirical Interactions for the Nuclear Shell Model: An Update
• Nonperturbative shell-model interactions from the in-medium similarity renormalization group
• Evolution of Nuclear Many-Body Forces with the Similarity Renormalization Group
• Is nuclear matter perturbative with low-momentum interactions?
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Converged ab initio calculations of heavy nuclei
• Bogoliubov Many-Body Perturbation Theory for Open-Shell Nuclei
• Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States
• Angular-momentum projection in coupled-cluster theory: structure of ${}^{34}$Mg
• Generator-coordinate reference states for spectra and $0\nu \beta \beta$ decay in the in-medium similarity renormalization group
• Multi-reference many-body perturbation theory for nuclei III -- Ab initio calculations at second order in PGCM-PT
• Natural orbitals for ab initio no-core shell model calculations
• Particle-number projected Bogoliubov coupled cluster theory. Application to the pairing Hamiltonian
• Neutron matter at finite temperature based on chiral effective field theory interactions
• ADG: Automated generation and evaluation of many-body diagrams I. Bogoliubov many-body perturbation theory
• \texttt{NuHamil}: A numerical code to generate nuclear two- and three-body matrix elements from chiral effective field theory
• Charge radius of the short-lived ${}^{68}$Ni and correlation with the dipole polarizability
• In-medium $k$-body reduction of $n$-body operators
• Computing the dipole polarizability of 48Ca with increased precision
• Bogoliubov many-body perturbation theory under constraint
• Normal ordering of three-nucleon interactions for ab initio calculations of heavy nuclei
• Towards heavy-mass ab initio nuclear structure: Open-shell Ca, Ni and Sn isotopes from Bogoliubov coupled-cluster theory
• Zero-pairing limit of Hartree-Fock-Bogoliubov reference states
• ADG: Automated generation and evaluation of many-body diagrams II. Particle-number projected Bogoliubov many-body perturbation theory
• Equation of state of superfluid neutron matter with low-momentum interactions
• Impact of correlations on nuclear binding energies

Cited by in corpus (1)

• Bayesian approach for many-body uncertainties in nuclear structure: Many-body perturbation theory for finite nuclei