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Résumé |
Since the pioneering work of Robledo [1], the Pfaffian has been
extensively studied in nuclear physics. With the use of the Grassmann
integrals, his work gives an excellent answer to the sign-problem in
the overlap between HFB wave functions (Onishi formula [2] proposed in
half a century ago). After Robledo's work, I have also studied some
extensions [3] and applications. Here I will talk about the following
topics:
\begin{enumerate}
\item Basics of Pfaffian and matrix elements of quantum many-body system
\item Pfaffian and sign-problem of Onishi formula
\begin{itemize}
\item Pfaffian formula for overlap of HFB wave functions
\item Origin of the sign-problem and liked cluster theorem
\end{itemize}
\item Pfaffian and Wick's theorem
\end{enumerate}
I will show some examples of Pfaffian in other fields of quantum
many-body physics.\\
\newline
[1] L.M. Robledo, Phys. Rev. C 79 (2009), 021302(R).\newline
[2] N. Onishi, S. Yoshida, Nucl. Phys. 80 (1966) 367.\newline
[3] M. Oi, T. Mizusaki, Phys. Lett. B 707 (2012) 305, T. Mizusaki, M.
Oi, Phys. Lett. B 715 (2012) 219,T. Mizusaki, M. Oi, F. Chen, Y. Sun,
Phys. Lett. B 725 (2013) 175, T.Mizusaki, M.Oi, N.Shimizu, Phys. Lett.
B779 (2018) 237. |
