Norm-overlap formula of Hartree-Fock-Bogoliubov states with odd number parity

Abstract

A formula to calculate a norm overlap between Hartree-Fock-Bogoliubov (HFB) states with the odd number parity (one quasi-particle excited states) is derived with help of the Grassmann numbers and the Fermion coherent states. The final form of the formula is expressed in terms of a product of the Pfaffian for a neighboring even-even system (the zero quasi-particle state), and an extra factor consisting of the Bogoliubov transformation matrix and the anti-symmetric matrix in Thouless' HFB ansatz for the even-even system.

14 pages (12pts), no figure

References in corpus (3)

• The sign of the overlap of HFB wave functions
• Generalized Wick's theorem for multiquasiparticle overlaps as a limit of Gaudin's theorem
• Technical aspects of the evaluation of the overlap of Hartree- Fock- Bogoliubov wave functions

Cited by in corpus (11)

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• Toward extremes of angular momentum: Application of the Pfaffian algorithm in realistic calculations
• Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states
• A new formulation to calculate general HFB matrix elements through Pfaffian
• The nuclear energy density functional formalism
• Why does the sign problem occur in evaluating the overlap of HFB wave functions?
• A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations
• Symmetry Restoration in Mixed-Spin Paired Heavy Nuclei
• A convenient implementation of the overlap between arbitrary Hartree-Fock-Bogoliubov vacua for projection