Nodal lines in the cranked HFB overlap kernels
Section snippets
Acknowledgments
We greatly thank Professor N. Onishi for giving us good insights through discussions in order to tackle the present problem. M.O. is grateful for discussions with Professors H. Flocard and P.-H. Heenen. Careful reading of the manuscript by Prof. P. Walker is acknowledged. Financial support from the Japanese Society for the Promotion of Sciences (JSPS) and an EPSRC advanced research fellowship GR/R75557/01 are appreciated by M.O. Parts of the numerical calculations were performed at the Centre
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2022, Progress in Particle and Nuclear PhysicsWhy does the sign problem occur in evaluating the overlap of HFB wave functions?
2018, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy PhysicsMatrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states
2014, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy PhysicsCitation Excerpt :The Onishi formula [4,5] is the first expression of the overlap between two different HFB vacua, but the sign of the overlap is not determined. Many works have been done to overcome this sign problem [6–14]. In Ref. [14], Robledo made the final solution and proposed a new formula using the Pfaffian rather than the determinant.
A convenient implementation of the overlap between arbitrary Hartree-Fock-Bogoliubov vacua for projection
2014, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy PhysicsCitation Excerpt :Unfortunately, the Onishi formula leaves the sign of the overlap undefined due to the square root of a determinant. Several efforts have been made to overcome this sign problem [11–16]. In 2009, Robledo proposed a different overlap formula with the Pfaffian rather than the determinant [17].
A new formulation to calculate general HFB matrix elements through the Pfaffian
2012, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy PhysicsCitation Excerpt :However, in an attempt to go beyond the mean-field description, especially in the case of three-dimensional angular momentum projection, there has been a difficulty originating from the long-standing problem in the phase determination of norm-overlap kernels through the Onishi formula [4]. This problem has been thoroughly investigated by many authors, for instance, in Refs. [4–8]. Many of them relied upon the analytic continuity approach for the phase determination, which can be carried out with the Onishi formula [4].
Norm-overlap formula for Hartree-Fock-Bogoliubov states with odd number parity
2012, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy PhysicsCitation Excerpt :Such a case was seen in the cranked HFB wave functions, and it was discovered that the so-called “nodal lines” (a collection of zeros of the overlap) are the source of the problem [4]. A method to overcome this problem was presented in Ref. [4], and an improvement to the method was recently found by the present authors [5]. With this method based on the Onishi formula, the sign problem was solved.