On the norm overlap between many-body states. I. Uncorrelated overlap between arbitrary Bogoliubov product states

Abstract

State-of-the-art multi-reference energy density functional calculations require the computation of norm overlaps between different Bogoliubov quasiparticle many-body states. It is only recently that the efficient and unambiguous calculation of such norm kernels has become available under the form of Pfaffians~[L. M. Robledo, Phys. Rev. C79, 021302 (2009)]. The goals of this work is (i) to propose and implement an alternative to the Pfaffian method to compute unambiguously the norm overlap between arbitrary Bogoliubov quasiparticle states and (ii) to extend the first point to explicitly correlated norm kernels at play in recently developped particle-number-restored Bogoliubov coupled-cluster (PNR-BCC) and particle-number-restored many-body perturbation (PNR-BMBPT) ab initio theories~[T. Duguet and A. Signoracci, J. Phys. G44, 015103 (2017)]. Point (i) constitutes the purpose of the present paper while point (ii) is addressed in a forthcoming companion paper. We generalize the method used in~[T. Duguet and A. Signoracci, J. Phys. G44, 015103 (2017)] to obtain the norm overlap between arbitrary Bogoliubov product states under a closed-form expression. The formula is physically intuitive, accurate, versatile and relies on elementary linear algebra operations. It equally applies to norm overlaps between Bogoliubov states of even or odd number parity. Numerical applications illustrate these features and provide a transparent representation of the content of the norm overlaps. Furthermore, the closed-form expression extends naturally to correlated overlaps at play in PNR-BCC and PNR-BMBPT. As such, the straight overlap between Bogoliubov states is the zeroth-order reduction of more involved norm kernels to be studied in the forthcoming paper.

25 pages, 6 figures

References in corpus (4)

• Particle-Number Projection and the Density Functional Theory
• The sign of the overlap of HFB wave functions
• Symmetry broken and restored coupled-cluster theory I. Rotational symmetry and angular momentum
• Technical aspects of the evaluation of the overlap of Hartree- Fock- Bogoliubov wave functions

Cited by in corpus (14)

• Symmetry restoration in mean-field approaches
• Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• In-medium $k$-body reduction of $n$-body operators
• Geminal replacement models based on AGP
• Variational approximations to exact solutions in shell-model valence spaces: calcium isotopes in the pf-shell
• A new and practical formulation for overlaps of Bogoliubov vacua
• Multiscale physics of atomic nuclei from first principles
• Why does the sign problem occur in evaluating the overlap of HFB wave functions?
• Ab initio computations from ${}^{78}$Ni towards ${}^{70}$Ca along neutron number $N=50$
• Symmetry-projected variational calculations with the numerical suite TAURUS II. Configuration mixing of symmetry-projected reference states
• Structure of odd-mass Ne, Na, and Mg nuclei
• Fock space representations of Bogolyubov transformations as spin representations
• Multi-reference many-body perturbation theory for nuclei I -- Novel PGCM-PT formalism