Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions

Area of Science:

• Quantum Many-Body Physics
• Computational Nuclear Physics

Background:

• Hartree-Fock-Bogoliubov (HFB) methods are crucial for nuclear structure but face numerical challenges.
• Standard Wick's theorem formulations encounter divisions by zero with nonorthogonal HFB wavefunctions.

Purpose of the Study:

• To develop a numerically robust formulation of Wick's theorem for HFB wavefunctions.
• To overcome limitations of existing methods for calculating matrix elements in many-body theories.

Main Methods:

• Introduced a new Wick's theorem formulation that handles nonorthogonal HFB states.
• Ensured cancellation between overlap zeros and Pfaffian poles for fermionic systems.
• Developed a computationally efficient version and a robust normalization procedure.

Main Results:

• The new formalism eliminates self-interaction and diverging normalization factors.
• Achieved robust symmetry-projected HFB calculations at mean-field cost.
• Demonstrated a stable and accurate solution for a challenging Jordan-Wigner Hamiltonian.

Conclusions:

• The robust Wick's theorem formulation significantly advances HFB-based many-body theories.
• Enables stable and efficient quantum calculations using quasiparticle vacuum states.
• Provides a unified treatment for even and odd particle numbers, reducing to Hartree-Fock.