Density-Functional Theory on Graphs

Abstract

The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn theorem is found void in general, while many insights into the topological structure of the density-potential mapping can be won. We give precise conditions for a ground state to be uniquely v-representable and are able to prove that this property holds for almost all densities. A set of examples illustrates the theory and demonstrates the non-convexity of the pure-state constrained-search functional.

References in corpus (28)

• Density-functionals not based on the electron gas: Local-density approximation for a Luttinger liquid
• Nonuniqueness of the Potentials of Spin-Density-Functional Theory
• Proof for an upper bound in fixed-node Monte Carlo for lattice fermions
• The Hubbard Dimer: A density functional case study of a many-body problem
• Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices
• Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model
• Time Dependent Density Functional Theory meets Dynamical Mean Field Theory: Real-Time Dynamics for the 3D Hubbard model
• Structure of fermion nodes and nodal cells
• Differentiable but exact formulation of density-functional theory
• Time-dependent V-representability on lattice systems
• Steady-State Density Functional Theory for Finite Bias Conductances
• Time-dependent current density functional theory on a lattice
• Time-dependent density functional theory on a lattice
• Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies
• Degeneracy in Density Functional Theory: Topology in v- and n-Space
• Nonuniqueness in spin-density-functional theory on lattices
• Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions
• One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures
• Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem
• Lattice density-functional theory on graphene
• Taming Density Functional Theory by Coarse-Graining
• Uniqueness of density-to-potential mapping for fermionic lattice systems
• Coarse-grained V-representability
• Exact Maps in Density Functional Theory for Lattice Models
• Mott metal-insulator transition from steady-state density functional theory
• Open problems in the spectral theory of signed graphs
• Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space
• The Graph of the Hypersimplex