Year: 2026
Type: article
Abstract: We prove that the Hilbert–Schmidt norm of k -particle reduced density matrices of N -body fermionic states is bounded from above by $$C_kN^{k/2}$$ C k N k / 2 - matching the scaling behaviour of Slater determinant states. This generalises a recent result of Christiansen [3] on 2-particle reduced density matrices to higher order density matrices. Moreover, our estimate directly yields a lower bound on the von Neumann entropy and the 2-Rényi entropy of reduced density matrices, thereby providing further insight into conjectures of Carlen–Lieb–Reuvers [2, 8].
Source: Annales Henri Poincaré
Author: François L. A. Visconti
Institution: Ludwig-Maximilians-Universität München
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7140138918