Friday, June 14, 2013

1306.3051 (Zao-Chun Gao et al.)

Overlap formula between the HFB vacua for the symmetry restoration    [PDF]

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.
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