Hilbert–Schmidt Estimates for Fermionic 2-Body Operators

Christiansen, Martin Ravn (2024): Hilbert–Schmidt Estimates for Fermionic 2-Body Operators. In: Communications in Mathematical Physics, Vol. 405, 18

Abstract

We prove that the 2-body operator γ2Ψ γ 2 Ψ of a fermionic N -particle state Ψ Ψ obeys ∥γ2Ψ∥HS≤5N ‖ γ 2 Ψ ‖ HS ≤ 5 N , which complements the bound of Yang (Rev Mod Phys 34:694, 1962) that ∥γ2Ψ∥op≤N ‖ γ 2 Ψ ‖ op ≤ N . This estimate furthermore resolves a conjecture of Carlen–Lieb–Reuvers (Commun Math Phys 344:655–671, 2016) concerning the entropy of the normalized 2-body operator. We also prove that the Hilbert–Schmidt norm of the truncated 2-body operator γ2Ψ,T γ 2 Ψ , T obeys the inequality ∥γ2Ψ,T∥HS≤5N tr (γ1Ψ(1−γ1Ψ)) ‖ γ 2 Ψ , T ‖ HS ≤ 5 N tr ( γ 1 Ψ ( 1 - γ 1 Ψ ) ) .

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0010-3616
• Language: English