https://doi.org/10.1140/epja/s10050-022-00843-2
Regular Article - Theoretical Physics
On the off-diagonal Wick’s theorem and Onishi formula
Alternative and consistent approach to off-diagonal operator and norm kernels
1
IRFU, CEA, Université Paris-Saclay, 91191, Gif-sur-Yvette, France
2
Department of Physics and Astronomy, Instituut voor Kern- en Stralingsfysica, KU Leuven, 3001, Leuven, Belgium
Received:
8
June
2022
Accepted:
21
September
2022
Published online:
18
October
2022
The projected generator coordinate method based on the configuration mixing of non-orthogonal Bogoliubov product states, along with more advanced methods based on it, require the computation of off-diagonal Hamiltonian and norm kernels. While the Hamiltonian kernel is efficiently computed via the off-diagonal Wick theorem of Balian and Brezin, the norm kernel relies on the Onishi formula (or equivalently the Pfaffian formula by Robledo or the integral formula by Bally and Duguet). Traditionally, the derivation of these two categories of formulae relies on different formal schemes. In the present work, the formulae for the operator and norm kernels are computed consistently from the same diagrammatic method. The approach further offers the possibility to address kernels involving more general states in the future.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
