A convenient implementation of the overlap between arbitrary Hartree-Fock-Bogoliubov vacua for projection

作者：Gao Zao Chun^*; Hu Qing Li; Chen Y S

来源：Physics Letters B, 2014, 732: 360-363.

DOI：10.1016/j.physletb.2014.04.012

• Hartree-Fock-Bogoliubov method
• Beyond mean field method
• Pfaffian

Overlap between Hartree-Fock-Bogoliubov (HFB) vacua is very important in the beyond mean-field calculations. However, in the HFB transformation, the U, V matrices are sometimes singular due to the exact emptiness (v(i) = 0) or full occupation (u(i) = 0) of some single-particle orbits. This singularity may cause some problem in evaluating the overlap between HFB vacua through Pfaffian. We found that this problem can be well avoided by setting those zero occupation numbers u(i), v(i) to some tiny values denoted by epsilon (> 0), which numerically satisfies 1 + epsilon(2) = 1 (e.g., s = 10(-8) when using the double precision data type). This treatment does not change the HFB vacuum state because u(i)(2), v(i)(2) = epsilon(2) are numerically zero relative to 1. Therefore, for arbitrary HFB transformation, we say that the U, V matrices can always be nonsingular. From this standpoint, we present a new convenient Pfaffian formula for the overlap between arbitrary HFB vacua, which is especially suitable for symmetry restoration. Testing calculations have been performed for this new formula. It turns out that our method is reliable and accurate in evaluating the overlap between arbitrary HFB vacua.

• 出版日期2014-5-1
• 单位中国原子能科学研究院