任意Hartree-Fock-Bogoliubov投影真空重叠的简便实现
A convenient implementation of the overlap between arbitrary Hartree-Fock-Bogoliubov vacua for projection
摘要：
Hartree-Fock-Bogoliubov（HFB）真空之间的重叠在超平均场计算中是非常重要的。然而，在HFB变换中，由于某些单粒子轨道的精确空（$v_i=0$）或完全占用（$u_i=0$），$U,V$矩阵有时是奇异的。这种奇异性可能会导致一些问题，在评估之间的重叠HFB真空通过Pfiran。我们发现，通过将这些零占用数设置为一些微小的值（例如，$u_i,v_i=10^{-8}$）。该处理不改变HFB真空状态，因为$u_i^2,v_i^2=10^{-16}$相对于1在数值上为零。因此，对于任意HFB变换，我们说$U,V$矩阵总是非奇异的。从这一观点出发，我们提出了一个新的方便的Pfiran公式之间的重叠任意HFB真空，这是特别适合于对称性恢复。对新公式进行了试算。结果表明，我们的方法是可靠的和准确的评估之间的重叠任意HFB真空。
英文摘要：
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 to some tiny values (e.g., $u_i,v_i=10^{-8}$). This treatment does not change the HFB vacuum state because $u_i^2,v_i^2=10^{-16}$ 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.
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