| Abstract 摘要 | Pfaffian is a pure mathematical concept which defines a value for a skew-symmetric matrix. In 2009, Pfaffian was firstly introduced into nuclear physics by Robledo [1],and the long-standing sign problem of overlap between Hartree-Fock-Bogoliubov vacua has been completely solved. After that, beyond mean-field theories have been substantially developed with Pfaffian. It has been recognized that Pfaffian has the same mathematical strucuture as the generalized Wick's theorem. Therefore, one may substantially reduce the computational cost in the calculations of overlaps between multi-qausiparticle states in beyond mean-filed methods.
Beyond mean-field methods have been widely used in various many-body quantum systems. However, there still are some problems to be solved in the implementation of beyond mean field calculations. Especially for systems with large number of particles, such as heavy nuclei, the efficiency of beyond mean field calculations becomes a very serious problem. Recently, we have tried to figure out a convenient way of calculating the overlap between arbitrary HFB vacua [2]. We also found some compact formulae for the matrix elements of physical operators (e.g. Hamiltonian) between arbitrary HFB multiquasiparticle states [3]. These formulae may reduce the computational time by several orders of magnitude when applied to many-body quantum system in a large Fock space.
[1] L.M. Robledo, Phys. Rev. C 79 (2009) 021302(R).
[2] Zao-Chun Gao, Qing-Li Hu, and Y. S. Chen, Phys. Lett. B 732 (2014) 360.
[3] Qing-Li Hu, Zao-Chun Gao, and Y. S. Chen, Phys. Lett. B 734 (2014) 162. |
