Projection after variation in the finite-temperature Hartree-Fock-Bogoliubov approximation

Fanto, P.

doi:10.1103/physrevc.96.051301

Cited by 5 publications

(4 citation statements)

References 22 publications

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“…In spite of these difficulties, the use of projected statistics proved to be advantageous over other techniques when applied in the spirit of projection after variation, that does not require the evaluation of the entropy (Fanto et al 2017). The intrinsic difficulty associated with the sign ambiguity in the evaluation of the partition function was addressed in Fanto et al (2017) in a time reversal preserving scenario and further generalized using the Pfaffian method (Robledo 2009) to the more general case involving time reversal breaking intrinsic states (Fanto 2017).…”

Section: Symmetry Restoration At Finite Temperaturementioning

confidence: 99%

Symmetry restoration in mean-field approaches

Sheikh

Dobaczewski

Ring

et al. 2021

J. Phys. G: Nucl. Part. Phys.

100

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The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Some examples are strongly interacting medium and heavy mass atomic nuclei and mesoscopic condensed matter systems. In this approach, the linear Schrödinger equation for the exact many-body wave function is mapped onto a non-linear one-body potential problem. This approximation, not only provides computationally very simple solutions even for systems with many particles, but due to the non-linearity, it also allows for obtaining solutions that break essential symmetries of the system, often connected with phase transitions. In this way, additional correlations are subsumed in the system. However, the mean-field approach suffers from the drawback that the corresponding wave functions do not have sharp quantum numbers and, therefore, many results cannot be compared directly with experimental data. In this article, we discuss general group-theory techniques to restore the broken symmetries, and provide detailed expressions on the restoration of translational, rotational, spin, isospin, parity and gauge symmetries, where the latter corresponds to the restoration of the particle number. In order to avoid the numerical complexity of exact projection techniques, various approximation methods available in the literature are examined. Applications of the projection methods are presented for simple nuclear models, realistic calculations in relatively small configuration spaces, nuclear energy density functional (EDF) theory, as well as in other mesoscopic systems. We also discuss applications of projection techniques to quantum statistics in order to treat the averaging over restricted ensembles with fixed quantum numbers. Further, unresolved problems in the application of the symmetry restoration methods to the EDF theories are highlighted in the present work.

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Section: Symmetry Restoration At Finite Temperaturementioning

confidence: 99%

Symmetry restoration in mean-field approaches

Sheikh

Dobaczewski

Ring

et al. 2021

J. Phys. G: Nucl. Part. Phys.

100

View full text Add to dashboard Cite

show abstract

“…We assume time-reversal symmetry; for a generalization to the case where time-reversal symmetry may be broken see Ref. [40].…”

Section: Canonical Partition Functions and Calculation Of State Densitiesmentioning

confidence: 99%

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

Ryssens

Alhassid

2021

Eur. Phys. J. A

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We present the code HF-SHELL for solving the self-consistent mean-field equations for configurationinteraction shell model Hamiltonians in the proton-neutron formalism. The code can calculate both zero-and finitetemperature properties in the Hartree-Fock (HF), HF+ Bardeen-Cooper-Schrieffer (HF+BCS) and the Hartree-Fock-Bogoliubov (HFB) mean-field approximations. Particlenumber projection after variation is incorporated to reduce the grand-canonical ensemble to the canonical ensemble, making the code particularly suitable for the calculation of nuclear state densities. The code does not impose axial symmetry and allows for triaxial quadrupole deformations. The self-consistency cycle is particularly robust through the use of the heavy-ball optimization technique and the implementation of different options to constrain the quadrupole degrees of freedom.

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“…We assume time-reversal symmetry; for a generalization to the case where time-reversal symmetry may be broken see Ref. [38].…”

Section: Canonical Partition Functions and Calculation Of State Densi...mentioning

confidence: 99%

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

Ryssens,

Alhassid

2020

Preprint

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We present the code HF-SHELL for solving the self-consistent mean-field equations for configurationinteraction shell model Hamiltonians in the proton-neutron formalism. The code can calculate both ground-state and finite-temperature properties in the Hartree-Fock (HF), HF+Bardeen-Cooper-Schrieffer (HF+BCS), and the Hartree-Fock-Bogoliubov (HFB) mean-field approximations. Particle-number projection after variation is incorporated to reduce the grand-canonical ensemble to the canonical ensemble, making the code particularly suitable for the calculation of nuclear state densities. The code does not impose axial symmetry and allows for triaxial quadrupole deformations. The selfconsistency cycle is particularly robust through the use of the heavy-ball optimization technique and the implementation of different options to constrain the quadrupole degrees of freedom.

show abstract

Projection after variation in the finite-temperature Hartree-Fock-Bogoliubov approximation

Cited by 5 publications

References 22 publications

Symmetry restoration in mean-field approaches

Symmetry restoration in mean-field approaches

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

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

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