Hilbert-Schmidt Estimates for Fermionic 2-Body Operators
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929230460223488 |
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| author | Christiansen, Martin Ravn |
| author_facet | Christiansen, Martin Ravn |
| contents | We prove that the 2-body operator $γ_2^Ψ$ of a fermionic $N$-particle state $Ψ$ obeys $||γ_2^Ψ||_{HS} \leq \sqrt{5} N$, which complements the bound of Yang that $||γ_2^Ψ||_{op} \leq N$. This estimate furthermore resolves a conjecture of Carlen-Lieb-Reuvers (arXiv:1403.3816) concerning the entropy of the normalized 2-body operator. We also prove that the Hilbert-Schmidt norm of the truncated 2-body operator $γ_2^{Ψ,T}$ obeys the inequality $||γ_2^{Ψ,T}||_{HS} \leq \sqrt{5 N \, \mathrm{tr}(γ_1^Ψ(1 - γ_1^Ψ))}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00834 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hilbert-Schmidt Estimates for Fermionic 2-Body Operators Christiansen, Martin Ravn Mathematical Physics Strongly Correlated Electrons We prove that the 2-body operator $γ_2^Ψ$ of a fermionic $N$-particle state $Ψ$ obeys $||γ_2^Ψ||_{HS} \leq \sqrt{5} N$, which complements the bound of Yang that $||γ_2^Ψ||_{op} \leq N$. This estimate furthermore resolves a conjecture of Carlen-Lieb-Reuvers (arXiv:1403.3816) concerning the entropy of the normalized 2-body operator. We also prove that the Hilbert-Schmidt norm of the truncated 2-body operator $γ_2^{Ψ,T}$ obeys the inequality $||γ_2^{Ψ,T}||_{HS} \leq \sqrt{5 N \, \mathrm{tr}(γ_1^Ψ(1 - γ_1^Ψ))}$. |
| title | Hilbert-Schmidt Estimates for Fermionic 2-Body Operators |
| topic | Mathematical Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2305.00834 |