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

We establish one-body reduced density matrix (1RDM) functional theory for the canonical ensemble in a finite basis set at an elevated temperature. Including temperature guarantees the differentiability of the universal functional by occupying all states and additionally not fully occupying the states in a fermionic system. We use the 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 < ni < 1 for all i) are uniquely v-representable up to a constant.

Automated summary

In this study, a one-body reduced density matrix (1RDM) functional theory is established for the canonical ensemble in a finite basis set at an elevated temperature. The inclusion of temperature ensures the differentiability of the universal functional by occupying all states and not fully occupying the states in a fermionic system. Using the convexity of the universal functional and invertibility of the potential-to-1RDM map, it is shown that the subgradient only contains one element that is equivalent to differentiability. This allows for the unique v-representability of all 1RDMs with a purely fractional occupation number spectrum (0 < ni < 1 for all i) up to a constant.