A new formulation to calculate general HFB matrix elements through Pfaffian

Abstract

A new formula is presented for the calculation of matrix elements between multi-quasiparticle Hartree-Fock-Bogoliubov (HFB) states. The formula is expressed in terms of the Pfaffian, and is derived by using the Fermion coherent states with Grassmann numbers. It turns out that the formula corresponds to an extension of generalized Wick's theorem and simplifies the combinatorial complexity resulting from practical applications of generalized Wick's theorem by unifying the transition density and the transition pairing tensor in the HFB theory. The resultant formula is simpler and more compact than the traditional description of matrix elements of general many-body operators. In addition, through the derivation of our new formula, we found that the Pfaffian version of the Lewis Carroll formula corresponds to the relation conjectrured by Balian and Brezin for the HFB theory in 1969.

7 pages, submitted to PLB

References in corpus (6)

• The sign of the overlap of HFB wave functions
• Symmetry restoration in Hartree-Fock-Bogoliubov based theories
• Evaluation of overlaps between arbitrary Fermionic quasiparticle vacua
• 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
• Norm-overlap formula of Hartree-Fock-Bogoliubov states with odd number parity

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• Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions
• Why does the sign problem occur in evaluating the overlap of HFB wave functions?
• Configuration Interaction with Antisymmetrized Geminal Powers
• A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations
• Accurate and precise quantum computation of valence two-neutron systems
• Four-body correlation embedded in antisymmetrized geminal power wave function
• Antisymmetrized Geminal Powers with Larger Chemical Basis Sets
• A convenient implementation of the overlap between arbitrary Hartree-Fock-Bogoliubov vacua for projection
• Fock space representations of Bogolyubov transformations as spin representations
• Generalization of Balian-Brezin decomposition for exponentials with linear fermionic part
• Raman spectroscopy of anyons in generic Kitaev spin liquids