arXiv 2008.018592020-08nucl-thcond-mat.supr-conphysics.chem-ph

有限温度Hartree-Fock-Bogoliubov理论的零配对和零温度极限

Zero-pairing and zero-temperature limits of finite temperature Hartree-Fock-Bogoliubov theory

Thomas Duguet, Wouter Ryssens

备注：: 16 pages, 5 figures
发表信息：: Phys. Rev. C 102, 044328 (2020)
DOI：: 10.1103/PhysRevC.102.044328

摘要：

最近，在arXiv：2006.02871中详细研究了Hartree-Fock-Bogoliubov（HFB）平均场论的零对极限。结果表明，这样的限制总是定义良好的任何粒子数A，但由此产生的多体描述不同的定性取决于系统是封闭的（子）壳或开放的（子）壳性质。在这里，我们将讨论扩展到更一般的框架的温度HFB（FTHFB）处理统计密度算子，而不是纯粹的多体状态。我们详细审查零温度和零配对限制这样的描述，特别是这两个限制的组合。对于闭壳层系统，我们发现FTHFB公式简化为（零温度）Hartree-Fock公式，即我们恢复了教科书的解决方案。然而，对于开壳层系统，所得到的描述取决于两个极限的顺序：如果首先执行零温度极限，FTHFB密度算符降级为纯态，这是有限数量的斯莱特行列式的线性组合，即arXiv：2006.02871的情况。如果先进行零配对限制，FTHFB密度算符仍然是有限数量的斯莱特行列式与非零熵的混合物，即使温度为零。这些分析结果说明了一系列的氧同位素的数值。

英文摘要：

Recently, the zero-pairing limit of Hartree-Fock-Bogoliubov (HFB) mean-field theory was studied in detail in arXiv:2006.02871. It was shown that such a limit is always well-defined for any particle number A, but the resulting many-body description differs qualitatively depending on whether the system is of closed-(sub)shell or open-(sub)shell nature. Here, we extend the discussion to the more general framework of Finite-Temperature HFB (FTHFB) which deals with statistical density operators, instead of pure many-body states. We scrutinize in detail the zero-temperature and zero-pairing limits of such a description, and in particular the combination of both limits. For closed-shell systems, we find that the FTHFB formulism reduces to the (zero-temperature) Hartree-Fock formulism, i.e. we recover the textbook solution. For open-shell systems, however, the resulting description depends on the order in which both limits are taken: if the zero-temperature limit is performed first, the FTHFB density operator demotes to a pure state which is a linear combination of a finite number of Slater determinants, i.e. the case of arXiv:2006.02871. If the zero-pairing limit is performed first, the FTHFB density operator remains a mixture of a finite number of Slater determinants with non-zero entropy, even as the temperature vanishes. These analytical findings are illustrated numerically for a series of Oxygen isotopes.

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