Cluster property and entanglement in the superconducting state
Abstract
We present the conditions for satisfying the cluster property in the superconducting state. Using these conditions, we show that the cluster property employed when deriving the order parameter of the superconducting state (OPSS) holds true, and that the OPSS is given by S⟨ Ψ| ψ̂(x)ψ̂(x') | Ψ⟩S, where |Ψ⟩S is the superconducting state, and where ψ̂(x) is the field operator of superconducting electrons. This provides a resolution to the long-standing concern raised by Leggett et al.\ regarding particle-number fluctuation in the superconducting state. In addition, by considering the entanglement between two particles composed of the maximum geminal of the BCS ground state [J.\ Phys. Commun. 5, 095003 (2021)], it is confirmed that the larger the deviation from the conditions for satisfying the cluster property becomes, the greater the magnitude of the entanglement becomes. This shows not only the effectiveness of the conditions for satisfying the cluster property but also the justification of the OPSS that has been commonly used.
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BibTeX
@misc{higuchi2026cluster,
title = {{Cluster property and entanglement in the superconducting state}},
author = {Katsuhiko Higuchi and Masahiko Higuchi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30581},
eprint = {2610.30581},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30581},
}
RIS
TY - UNPB
TI - Cluster property and entanglement in the superconducting state
AU - Katsuhiko Higuchi
AU - Masahiko Higuchi
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30581
UR - https://arxiv.org/abs/2610.30581
AB - We present the conditions for satisfying the cluster property in the superconducting state. Using these conditions, we show that the cluster property employed when deriving the order parameter of the superconducting state (OPSS) holds true, and that the OPSS is given by _S⟨ Ψ| ψ̂(x)ψ̂(x') | Ψ⟩_S, where |Ψ⟩_S is the superconducting state, and where ψ̂(x) is the field operator of superconducting electrons. This provides a resolution to the long-standing concern raised by Leggett et al.\ regarding particle-number fluctuation in the superconducting state. In addition, by considering the entanglement between two particles composed of the maximum geminal of the BCS ground state [J.\ Phys. Commun. 5, 095003 (2021)], it is confirmed that the larger the deviation from the conditions for satisfying the cluster property becomes, the greater the magnitude of the entanglement becomes. This shows not only the effectiveness of the conditions for satisfying the cluster property but also the justification of the OPSS that has been commonly used.
ER -