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arXiv · 2209.11663

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

Sarina M. Sutter·Klaas J. H. Giesbertz
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Abstract

We establish one-body reduced density-matrix functional theory for the canonical ensemble in a finite basis set at an 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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Sarina M. Sutter, Klaas J. H. Giesbertz. 2022-09-23. One-body reduced density-matrix functional theory for the canonical ensemble. https://doi.org/10.1103/physreva.107.022210

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