One-body reduced density-matrix functional theory for the canonical ensemble

• URL: http://arxiv.org/abs/2209.11663v2
• Date: Thu, 6 Oct 2022 13:17:02 GMT
• Title: One-body reduced density-matrix functional theory for the canonical ensemble
• Authors: Sarina M. Sutter and Klaas J. H. Giesbertz
• Abstract summary: Including temperature guarantees differentiability of the universal functional by occupying all states and additionally not fully occupying the states in a fermionic system. We use convexity of the universal functional and invertibility of the potential-to-1RDM map to show that the subgradient contains only one element which is equivalent to differentiability.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We establish one-body reduced density-matrix functional theory for the canonical ensemble in a finite basis set at elevated temperature. Including temperature guarantees differentiability of the universal functional by occupying all states and additionally not fully occupying the states in a fermionic system. We use convexity of the universal functional and invertibility of the potential-to-1RDM map to show that the subgradient contains only one element which is equivalent to differentiability. This allows us to show that all 1RDMs with a purely fractional occupation number spectrum ($0 < n_i < 1 \; \forall_i$) are uniquely $v$-representable up to a constant.

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