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

TL;DR

This paper develops a finite-basis, temperature-inclusive one-body reduced density-matrix functional theory for the canonical ensemble, ensuring differentiability and unique v-representability of fractional occupation states.

Contribution

It introduces a temperature-dependent framework for 1RDM functional theory in the canonical ensemble, proving differentiability and unique v-representability of fractional occupation states.

Findings

Universal functional is differentiable at finite temperature.

All 1RDMs with fractional occupations are uniquely v-representable.

Convexity and invertibility are key to the theoretical results.

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.