Bogoliubov many-body perturbation theory for open-shell nuclei

Abstract

A novel Rayleigh-Schrödinger many-body perturbation theory (MBPT) approach is introduced by making use of a particle-number-breaking Bogoliubov reference state to tackle (near-)degenerate open-shell fermionic systems. By choosing a reference state that solves the Hartree-Fock-Bogoliubov variational problem, the approach reduces to the well-tested Møller-Plesset, i.e., Hartree-Fock based, MBPT when applied to closed-shell systems. Due to its algorithmic simplicity, the newly developed framework provides a computationally simple yet accurate alternative to state-of-the-art non-perturbative many-body approaches. At the price of working in the quasi-particle basis associated with a single-particle basis of sufficient size, the computational scaling of the method is independent of the particle number. This paper presents the first realistic applications of the method ranging from the oxygen to the nickel isotopic chains on the basis of a modern nuclear Hamiltonian derived from chiral effective field theory.

Normal-ordered k-body approximation in particle-number-breaking theories

“…In any case, the NO2B approximation has been employed so far on the basis of symmetry-conserving states. Only recently such an approximation has been employed in Bogoliubov MBPT (BMBPT) [4,29] in which U(1) symmetry associated with particle-number conservation is spontaneously broken by the (approximate) many-body state. In this context, the normal ordering of operators at play is performed with respect to a particle-numberbreaking Bogoliubov reference state such that proceeding to a naive truncation may lead to approximating a particle-number-conserving operator by a particlenumber-breaking one.…”

Improved many-body expansions from eigenvector continuation

“…Thus, BMBPT qualifies as a perturbation theory under constraint [48]. sophisticated non-perturbative many-body schemes on a few percents level at a small fraction of the computational cost [16]. The second application is thus dedicated to the openshell nucleus 18 O and employs the soft interaction characterized by the SRG parameter λ = 2.0 fm −1 .…”

“…Subsequently, the many-body basis of H 0 used to expand perturbative state corrections is limited to configurations obtained via two-, four-and selected [50] six-quasiparticle excitations of the reference state. 3 The latter truncation leads to performing approximate BMBPT calculations at order P ≥ 3 where basis 2 A converged ab initio calculation with respect to the size of the one-body basis would typically require emax = 2n + l = 13 [16]. 3 This corresponds to limiting the configuration space to oneparticle/one-hole, two-particle/two-hole and selected threeparticle/three-hole excitations when using a simpler Slater determinant reference state.…”

Renormalization of pionless effective field theory in the A-body sector

“…Less trivial are partitionings breaking U (1) symmetry that are employed to tackle the superfluid character of nuclear matter and open-shell nuclei, e.g. MBPT [43,30,44], CC [45] or SCGF [46,23] using a Bogoliubov vacuum as reference state. The associated diagrammatic relies on the use of anomalous propagators in addition to normal propagators.…”

“…Typical truncations applicable to A-body systems with A 10 are nowadays implemented on the basis of nonperturbative self-consistent Green's function (SCGF) [21,22,23], coupled cluster (CC) [24,25] and in-medium similarity renormalization group (IM-SRG) [26,27] methods but also on the basis of MBPT [28,29,30].…”