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

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.