Relation between Pfaffian and HFB-type projected quasi-particle wave function

The restoration of particle number and angular momentum symmetry using projection operators has been theoretically investigated for mean-field Hartree-Fock-Bogoliubov (HFB) states. A computer code for the projection of particle number was then implemented. To do so efficiently and avoid the sign ambiguity of the Onishi formula, the computation of overlap between quasi-particle vaccums using Pfaffians was investigated. Different algorithms for the the Pfaffian from~\cite{GBBertschRobledo},\cite{Wimmer}, was tested for performance and accuracy. For the same reason different truncations of the model space was also investigated. The particle number projector was then implemented in \textit{HOSPHE} \cite{Carlsson} for calculations of ground states pertaining to an effective Quadrupole plus Pairing Hamiltonian calculated using the SLy4 parametrization of the Skyrme interaction.The restoration of particle number and angular momentum symmetry using projection operators has been theoretically investigated for mean-field Hartree-Fock-Bogoliubov (HFB) states. A computer code for the projection of particle number was then implemented. To do so efficiently and avoid the sign ambiguity of the Onishi formula, the computation of overlap between quasi-particle vaccums using Pfaffians was investigated. Different algorithms for the the Pfaffian from~\cite{GBBertschRobledo},\cite{Wimmer}, was tested for performance and accuracy. For the same reason different truncations of the model space was also investigated. The particle number projector was then implemented in \textit{HOSPHE} \cite{Carlsson} for calculations of ground states pertaining to an effective Quadrupole plus Pairing Hamiltonian calculated using the SLy4 parametrization of the Skyrme interaction.

Jan 1, 20190 citations

Overlap formula between the HFB vacua for the symmetry restoration

Zao-Chun Gao, Qing-Li Hu, Y. S. Chen

Using the Pfaffian identity, the formula for the overlap between Hartree-Fock-Bogoliubov (HFB) vacua, recently proposed by Bertsch and Robledo [Phys. Rev. Lett. {\bf 108}, 042505(2012)] is deduced into a simpler form. This new formula does not explicitly depend on the Bloch-Messiah decomposition of the HFB transformation, but it requires the existence of the $V^{-1}$ matrix. It presents the significant convenience of application for the symmetry restoration in the wave functions of general Bogoliubov form. Numerical calculations show that this formula is able to reproduce the results of the Onishi formula with the same accuracy as well as having the correct sign. It is also shown that a small number of the integrating mesh points ( $N_\text{mesh}=16$ ) is enough to perform the particle number projection even for the heavy nuclear system.Using the Pfaffian identity, the formula for the overlap between Hartree-Fock-Bogoliubov (HFB) vacua, recently proposed by Bertsch and Robledo [Phys. Rev. Lett. {\bf 108}, 042505(2012)] is deduced into a simpler form. This new formula does not explicitly depend on the Bloch-Messiah decomposition of the HFB transformation, but it requires the existence of the $V^{-1}$ matrix. It presents the significant convenience of application for the symmetry restoration in the wave functions of general Bogoliubov form. Numerical calculations show that this formula is able to reproduce the results of the Onishi formula with the same accuracy as well as having the correct sign. It is also shown that a small number of the integrating mesh points ($N_\text{mesh}=16$) is enough to perform the particle number projection even for the heavy nuclear system.

Jun 13, 20130 citations

Physics of projected wavefunctions

Claudius Gros

Annals of PhysicsJan 1, 1989284 citations

Physics of projected wavefunctions

Annals of PhysicsNov 1, 19881 citation

V^{-1}

matrix. It presents the significant convenience of application for the symmetry restoration in the wave functions of general Bogoliubov form. Numerical calculations show that this formula is able to reproduce the results of the Onishi formula with the same accuracy as well as having the correct sign. It is also shown that a small number of the integrating mesh points (

N_\text{mesh}=16

) is enough to perform the particle number projection even for the heavy nuclear system.