A convenient implementation of the overlap between arbitrary Hartree–Fock–Bogoliubov vacua for projection
A convenient implementation of the overlap between arbitrary Hartree–Fock–Bogoliubov vacua for projection
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DOI：
10.1016/j.physletb.2014.04.012
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发表时间：
2013-06
影响因子：
4.4
通讯作者：
Zao-Chun Gao;Qingmei Hu;Y. S. Chen
中科院分区：
文献类型：
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作者：
Zao-Chun Gao;Qingmei Hu;Y. S. Chen
摘要 Hartree-Fock-Bogoliubov (HFB) 真空之间的重叠在超平均场计算中非常重要。然而，在HFB变换中，由于某些单粒子轨道完全为空(v i= 0)或完全占据(u i= 0)，U、V矩阵有时是奇异的。这种奇点可能会导致在通过普法夫评估 HFB 真空之间的重叠时出现一些问题。我们发现，通过将这些零占用数 u i 、 vi 设置为一些用 ε (> 0) 表示的微小值，可以很好地避免这个问题，这在数值上满足 1+ ε 2= 1 （例如，使用双精度数据类型时，ε= 10− 8 ）。这种处理不会改变 HFB 真空状态，因为 u i 2, vi 2= ε 2 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。从这个角度来看，我们提出了一种新的方便的普法夫公式，用于任意 HFB 真空之间的重叠，该公式特别适合对称性恢复。已经对这个新公式进行了测试计算。事实证明，我们的方法在评估任意 HFB 真空之间的重叠方面是可靠且准确的。
Abstract 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 ε (> 0), which numerically satisfies 1+ ε 2= 1 (eg, ε= 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= ε 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.