Finite-temperature mean-field approximations for shell model Hamiltonians: the code HF-SHELL

Ryssens, W.; Alhassid, Y.

doi:10.48550/arxiv.2009.01205

Cited by 1 publication

(3 citation statements)

References 42 publications

(81 reference statements)

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“…Given that the exact solution ( 5) is intractable for any realistic Hamiltonian, approximations must be formulated. The mean-field FTHFB approximation consists of using a trial density operator of the form 6…”

Section: Hartree-fock-bogoliubov Approximationmentioning

confidence: 99%

“…( 3) and ( 4), the uppercase Tr indicates a many-body trace over Fock space, while the lower case tr will be used to indicate traces over the one-body Hilbert space. 6 A partition function associated with D can be defined but it is not equal to Z given that the derivatives of the latter do not satisfy thermodynamic consistency relations [4,6].…”

Section: ≡mentioning

confidence: 99%

“…Oxygen isotopes are described as having an inert core of 16 O, implying that the protons play no role and that 18 O, 19 O, 22 O, and 26 O possess 2, 3, 6, and 10 active valence neutrons, respectively. The working equations are solved on the basis of the HF-SHELL code [6]. In the present context, virtually all sd-shell nuclei exhibit a deformed mean-field minimum and several of them are triaxial [11].…”

Section: A Numerical Setupmentioning

confidence: 99%

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

Duguet

Ryssens

2020

Phys. Rev. C

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Background: Recently, variational Hartree-Fock-Bogoliubov (HFB) mean-field equations were shown to possess a mathematically well-defined zero-pairing limit, independently of the closed-or open-shell character of the system under consideration. This limit is nontrivial for open-shell systems such that HFB theory does not reduce to the Hartree-Fock (HF) formalism in all cases. Purpose: The present work extends this analysis to finite-temperature HFB (FTHFB) theory by investigating the behavior of this more general formalism in the combined zero-temperature and zero-pairing limits. Methods: The zero-pairing and zero-temperature limits of the FTHFB statistical density operator constrained to carry an arbitrary (integer) number of particles A on average is worked out analytically and realized numerically using a two-nucleon interaction. Results: While the FTHFB density operator reduces to the projector corresponding to a pure HF Slater determinant for closed-shell nuclei, the FTHFB formalism does not reduce to the HF theory in all cases in the zero-temperature and zero-pairing limits, i.e., for open-shell nuclei. However, the fact that a nucleus can be of open-shell character in these joint limits is necessarily the result of some symmetry restrictions. Whenever it is the case, the nontrivial description obtained for open-shell systems is shown to depend on the order with which both limits are taken, i.e., the two limits do not commute for these systems. When the zero-temperature limit is performed first, the FTHFB density operator is demoted to a projector corresponding to a pure state made out of a linear combination of a finite number of Slater determinants with different (even) numbers of particles. When the zero-pairing limit is performed first, the FTHFB density operator remains a statistical mixture of a finite number of Slater determinants with both even and odd particle numbers. While the entropy (pairing density) is zero in the first (second) case, it does not vanish in the second (first) case in spite of the temperature (pairing) tending towards zero. The difference between both limits can have striking consequences for the (thermal) expectation values of observables. For instance, the particle-number variance does not vanish in either case and has limiting values that differ by a factor of two in both cases. Conclusions: While in the textbook situation associated with closed-shell nuclei Hartree-Fock-Bogoliubov (finite-temperature Hartree-Fock) theory reduces to Hartree-Fock theory in the zero-pairing (zero-temperature) limit, the present analysis demonstrates that a nontrivial and unexpected limit is obtained for this formalism in open-shell systems. This result sheds a new light on certain aspects of this otherwise very well-studied many-body formalism.

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Section: Hartree-fock-bogoliubov Approximationmentioning

confidence: 99%

Section: ≡mentioning

confidence: 99%