The variational Hartree-Fock-Bogoliubov (HFB) mean-field theory is the starting point of various (ab initio) many-body methods dedicated to superfluid systems. While taking the zero-pairing limit of HFB equations constitutes a text-book problem when the system is of closed-(sub)shell character, it is typically, although wrongly, thought to be ill-defined whenever the naive filling of single-particle levels corresponds to an open-shell system. The present work demonstrates that the zero-pairing limit of an HFB state is mathematically well-defined, independently of the closed- or open-shell character of the system in the limit. Still, the nature of the limit state strongly depends on the underlying shell structure and on the associated naive filling reached in the zero-pairing limit for the particle number A of interest. All the analytical findings are confirmed and illustrated numerically. While HFB theory has been intensively scrutinized formally and numerically over the last decades, it still uncovers unknown and somewhat unexpected features. From this general perspective, the present analysis demonstrates that HFB theory does not reduce to Hartree-Fock theory even when the pairing field is driven to zero in the HFB Hamiltonian matrix.

中文翻译：

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Hartree-Fock-Bogoliubov 参考状态的零对极限

变分 Hartree-Fock-Bogoliubov (HFB) 平均场理论是专用于超流体系统的各种（从头算）多体方法的起点。虽然当系统具有闭（子）壳特征时，采用 HFB 方程的零对极限构成教科书问题，但通常，尽管错误地认为，每当单粒子的幼稚填充时，它通常被认为是不明确的。级别对应于开壳系统。目前的工作表明，HFB 状态的零配对极限在数学上是明确定义的，与极限中系统的封闭或开放壳特征无关。尽管如此，极限状态的性质在很大程度上取决于底层壳结构和相关的初始填充，在零对极限中达到的目标粒子数 A。所有的分析结果都得到了证实和数字说明。虽然 HFB 理论在过去的几十年里受到了形式上和数值上的深入审查，但它仍然揭示了未知和有些出乎意料的特征。从这个一般的角度来看，本分析表明，即使在 HFB 哈密顿矩阵中的配对场被驱动为零时，HFB 理论也不会归结为 Hartree-Fock 理论。