Erratum: Thermal pairing treatment within the path integral formalism [Chin. Phys. C, 48 (11): 114102 (2024)]

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M. Fellah, N.H. Allal and M.R. Oudih. Erratum: Thermal pairing treatment within the path integral formalism [Chin. Phys. C, 48 (11): 114102 (2024)][J]. Chinese Physics C. doi: 10.1088/1674-1137/ae18a9
M. Fellah, N.H. Allal and M.R. Oudih. Erratum: Thermal pairing treatment within the path integral formalism [Chin. Phys. C, 48 (11): 114102 (2024)][J]. Chinese Physics C.  doi: 10.1088/1674-1137/ae18a9 shu
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Received: 2025-10-22
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Erratum: Thermal pairing treatment within the path integral formalism [Chin. Phys. C, 48 (11): 114102 (2024)]

  • Laboratoire de Physique Théorique- Faculté de Physique- USTHB, BP32 El-Alia, 16111 Bab-Ezzouar - Algiers - ALGERIA

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  • The paragraph between equations (A9) and (A11) in Appendix A on page 10 of the published version is partially incorrect. In particular, the formal expression of the operator $ {\cal{S}}_{j} $ is incomplete. This paragraph should then be read as follows:

    $ \begin{aligned} {\rm i} {\cal{S}}_{j}=\exp\left[ {\rm i}\frac{\pi}{2}\left( a_{j}+a_{j}^+\right) \right] \exp\left[ {\rm i}\frac{\pi}{2}\left( a_{\widetilde{_{j}}}+a_{\widetilde {j}}^+\right) \right] . \end{aligned}$

    (A9)

    That is,

    $ \begin{aligned} {\cal{S}}_{j}=\exp\left[ {\rm i} \frac{\pi}{2}\left( a_{j}+a_{j}^+ +a_{\widetilde{_{j}}}+a_{\widetilde{j}}^+-\frac{\pi}{2}S_{j}-1\right) \right] \end{aligned}$

    (A10)

    where we used the Glauber identity.

    And therefore

    $ \begin{aligned} U=\exp\left[ {\rm i}\frac{\pi}{2}\sum\limits_{j}\left( a_{j}+a_{j}^+ +a_{\widetilde{_{j}}}+a_{\widetilde{j}}^+-\frac{\pi}{2}S_{j}-1\right) \right] . \end{aligned}$

    (A11)

    It should be noted that this has no effect on the remainder of the calculations since we used the form given in Eq. (6) for $ {\cal{S}}_{j} $.

    The authors apologize for any inconvenience caused.

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