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

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.

arXiv comment7 pages, 1 figure

References in corpus (7)

• T>0 ensemble state density functional theory revisited
• Bose-Einstein Condensation, Fluctuations, and Recurrence Relations in Statistical Mechanics
• Observation of Interactions between Trapped Ions and Ultracold Rydberg Atoms
• The Kohn-Sham system in one-matrix functional theory
• Theory of Non-Interacting Fermions and Bosons in the Canonical Ensemble
• One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures
• Bose-Einstein condensation in the canonical ensemble

Cited by in corpus (6)

• Refining and relating fundamentals of functional theory
• Solution of the v-representability problem on a one-dimensional torus
• Extracting Many-Body Quantum Resources within One-Body Reduced Density Matrix Functional Theory
• A toolbox of spin-adapted generalized Pauli constraints
• v-Representability on a one-dimensional torus at elevated temperatures
• Refining ensemble $N$-representability of one-body density matrices from partial information