Sign of the overlap of Hartree-Fock-Bogoliubov wave functions

Robledo, L. M.

doi:10.1103/physrevc.79.021302

Cited by 131 publications

(186 citation statements)

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“…This treatment brings a complication in the evaluation of the norm overlap, which has been a nuisance for long time [3]. A breakthrough came recently to remove all the mathematical difficulties related to the square root operation (sign problem) in the know formulae, which was brought by Robledo with the Pfaffian [4],…”

Section: The Hartree-fock-bogoliubov Ansatzmentioning

confidence: 99%

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New Pfaffian formulae for an overlap of multiple quasiparticle states

Mizusaki

2014

EPJ Web of Conferences

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Section: The Hartree-fock-bogoliubov Ansatzmentioning

confidence: 99%

“…[7] (for the first three terms of one-body parts in Eq. (12)) and Robledo's original Pfaffian formula [4] (for the last two terms in Eq.(12). By combining the above results, one can evaluate the energy expectation value Ψ 0 |Ĥ|Ψ 0 in the Pfaffian form.…”

Section: An Application Of the Pfaffian Formulae: Calculation Of ĥmentioning

confidence: 99%

New Pfaffian formulae for an overlap of multiple quasiparticle states

Mizusaki

2014

EPJ Web of Conferences

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“…For the density operators considered in Ref. [1], e −tr[Y]/2 is real and positive because the expectation value of a density operator in any state is real and positive. The operator e 1 2 η † C(β,Ω)η does not have this property, so we must determine δ directly.…”

mentioning

confidence: 99%

“…Specifically, we extend the Pfaffian formula for the many-body traces of (unprojected) HFB density operators introduced by L. M. Robledo in Ref. [1] to evaluate the more complicated traces required in the PAV calculation. The Pfaffian is the square root of the determinant of a skewsymmetric matrix with a well-determined sign (see Appendix A of Ref.…”

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

Fanto

2017

Phys. Rev. C

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The finite-temperature Hartree-Fock-Bogoliubov (HFB) approximation often breaks symmetries of the underlying many-body Hamiltonian. Restricting the calculation of the HFB partition function to a subspace with good quantum numbers through projection after variation restores some of the correlations lost in breaking these symmetries, although effects of the broken symmetries such as sharp kinks at phase transitions remain. However, the most general projection after variation formula in the finite-temperature HFB approximation is limited by a sign ambiguity. Here, we extend the Pfaffian formula for the many-body traces of HFB density operators introduced by L. M. Robledo in Ref.[1] to eliminate this sign ambiguity and evaluate the more complicated many-body traces required in projection after variation in the most general HFB case. We validate our method through a proof-of-principle calculation of the particle-number-projected HFB thermal energy in a simple model.Introduction.-The Hartree-Fock-Bogoliubov (HFB) approximation is an important mean-field method for studying many-fermion systems in which pairing correlations are important. When extended to finite temperature [2], this method provides an efficient way to calculate statistical observables. The finite-temperature HFB approximation has been widely applied to study the deformation and pairing properties of nuclei [3,4] and is also useful for the study of atomic Fermi gases [5]. However, the finite-temperature HFB approximation often breaks symmetries of the underlying many-body Hamiltonian. In particular, the HFB approximation explicitly violates particle-number conservation if the pairing field is nonzero and can also violate rotational invariance when the mean-field solution is deformed. Breaking these symmetries reduces the accuracy of HFB predictions of statistical properties such as nuclear level densities [6].

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The Nuclear Energy Density Functional Formalism

Duguet

2014

Lecture Notes in Physics

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The present document focuses on the theoretical foundations of the nuclear energy density functional (EDF) method. As such, it does not aim at reviewing the status of the field, at covering all possible ramifications of the approach or at presenting recent achievements and applications. The objective is to provide a modern account of the nuclear EDF formalism that is at variance with traditional presentations that rely, at one point or another, on a Hamiltonian-based picture. The latter is not general enough to encompass what the nuclear EDF method represents as of today. Specifically, the traditional Hamiltonian-based picture does not allow one to grasp the difficulties associated with the fact that currently available parametrizations of the energy kernel E[g ′ , g] at play in the method do not derive from a genuine Hamilton operator, would the latter be effective. The method is formulated from the outset through the most general multi-reference, i.e. beyond mean-field, implementation such that the single-reference, i.e. "mean-field", derives as a particular case. As such, a key point of the presentation provided here is to demonstrate that the multi-reference EDF method can indeed be formulated in a mathematically meaningful fashion even if E[g ′ , g] does not derive from a genuine Hamilton operator. In particular, the restoration of symmetries can be entirely formulated without making any reference to a projected state, i.e. within a genuine EDF framework. However, and as is illustrated in the present document, a mathematically meaningful formulation does not guarantee that the formalism is sound from a physical standpoint. The price at which the latter can be enforced as well in the future is eventually alluded to.

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Sign of the overlap of Hartree-Fock-Bogoliubov wave functions

Cited by 131 publications

References 17 publications

New Pfaffian formulae for an overlap of multiple quasiparticle states

New Pfaffian formulae for an overlap of multiple quasiparticle states

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

The Nuclear Energy Density Functional Formalism

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