Relating the pure and ensemble density matrix functional

Abstract

A crucial theorem in Reduced Density Matrix Functional Theory (RDMFT) suggests that the universal pure and ensemble functional coincide on their common domain of pure N-representable one-matrices. We refute this by a comprehensive analysis of the geometric picture underlying Levy's constrained search. Moreover, we then show that the ensemble functional follows instead as the lower convex envelop of the pure functional. It is particularly remarkable that the pure functional determines the ensemble functional even outside its own domain of pure N-representable one-matrices. From a general perspective, this demonstrates that relaxing pure RDMFT to ensemble RDMFT does not necessarily circumvent the complexity of the one-body pure N-representability conditions (generalized Pauli constraints). Instead, the complexity may simply be transferred from the underlying space of pure N-representable one-matrices to the structure of the universal one-matrix functional.

version as published in Communications of Journal of Chemical Physics

References in corpus (10)

• Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory
• Structure of Fermionic Density Matrices: Complete N-representability Conditions
• Quantum marginal problem and N-representability
• The Pauli principle revisited
• Benchmark calculations for reduced density-matrix functional theory
• Performance of one-body reduced density matrix functionals for the homogeneous electron gas
• Landscape of an exact energy functional
• Information geometry of density matrices and state estimation
• Comment on some results of Erdahl and the convex structure of reduced density matrices
• Quantum codes give counterexamples to the unique pre-image conjecture of the N-representability problem

Cited by in corpus (33)

• Non-equilibrium Steady State Conductivity in Cyclo[18]carbon and Its Boron Nitride Analogue
• Diverging exchange force and form of the exact density matrix functional
• Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle
• Foundation of one-particle reduced density matrix functional theory for excited states
• Reduced Density Matrix Functional Theory for Bosons
• Refining and relating fundamentals of functional theory
• Unity of Kohn-Sham Density Functional Theory and Reduced Density Matrix Functional Theory
• Reduced Density Matrix Functional Theory for Superconductors
• An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
• Towards a Resolution of the Static Correlation Problem in Density Functional Theory from Semidefinite Programming
• Deriving density-matrix functionals for excited states
• Capturing static and dynamic correlation with $\Delta \text{NO}$-MP2 and $\Delta \text{NO}$-CCSD
• Exploiting the hessian for a better convergence of the SCF RDMFT procedure
• What Can Quantum Information Theory Offer to Quantum Chemistry?
• On the time evolution of fermionic occupation numbers
• 1-matrix functional for long-range interaction energy of two hydrogen atoms
• Implications of pinned occupation numbers for natural orbital expansions. I: Generalizing the concept of active spaces
• Implications of the unitary invariance and symmetry restrictions on the development of proper approximate one-body reduced density matrix functionals
• Functional Theory for Bose-Einstein Condensates
• Softmax parameterization of the occupation numbers for natural orbital functionals based on electron pairing approaches
• Assessing the Orbital-Optimized Unitary Ansatz for Density Cumulant Theory
• Insights into one-body density matrices using deep learning
• Orbital-Free Quasi-Density Functional Theory
• Determining the N-representability of a reduced density matrix via unitary evolution and stochastic sampling
• A toolbox of spin-adapted generalized Pauli constraints
• Impact of Parametrizations of the One-Body Reduced Density Matrix on the Energy Landscape
• Determining the ensemble N-representability of Reduced Density Matrices
• Solving one-body ensemble N-representability problems with spin
• Repulsively diverging gradient of the density functional in the Reduced Density Matrix Functional Theory
• Capturing electron correlation at mean-field cost: Assessment of i-DMFT and the underlying correlation conjecture
• Density-matrix functional theory of the attractive Hubbard model: Statistical analogy of pairing correlations
• Cumulants as the Variables of Density Cumulant Theory: A Path to Hermitian Triples
• Refining ensemble $N$-representability of one-body density matrices from partial information