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

TL;DR

This paper investigates the zero-temperature and zero-pairing limits of finite-temperature Hartree-Fock-Bogoliubov theory, revealing different behaviors for closed-shell and open-shell systems and their implications for nuclear structure modeling.

Contribution

It extends the analysis of zero-pairing limits to finite-temperature HFB, highlighting the order-dependent behavior of the density operator in open-shell systems.

Findings

For closed-shell systems, FTHFB reduces to Hartree-Fock at zero temperature.

Open-shell systems exhibit order-dependent limits, with different resulting states.

Numerical illustrations provided for Oxygen isotopes.

Abstract

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.