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arXiv:2505.21167

A Correlational Bound for Eigenvalues of Fermionic 2-Body Operators

Martin Ravn Christiansen

Published May 27, 2025• 0 citations
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Abstract

We prove that the eigenvalues of a 2-body operator $γ_{2}^Ψ$ associated to a fermionic $N$-particle state $Ψ$ are highly constrained by the structure of the corresponding eigenvectors: If $Φ=\sum_{k=1}^{\infty}λ_{k}u_{k}\wedge v_{k}$ is the canonical form of an eigenvector $Φ$ with eigenvalue $Λ$, then $Λ\leq(1+\frac{N-2}{2}\sum_{k=1}^{\infty}λ_{k}^{4})^{-1}N$. We also prove a lower bound on $\sup_{\Vert Ψ\Vert =1}\langle Φ,γ_{2}^ΨΦ\rangle$ for fixed $Φ$, and state a conjecture motivated by these results.

DOI
10.48550/arxiv.2505.21167

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