Kinetic-Energy Density-Functional Theory on a Lattice

Abstract

We present a kinetic-energy density-functional theory and the corresponding kinetic-energy Kohn-Sham (keKS) scheme on a lattice and show that by including more observables explicitly in a density-functional approach already simple approximation strategies lead to very accurate results. Here we promote the kinetic-energy density to a fundamental variable along side the density and show for specific cases (analytically and numerically) that there is a one-to-one correspondence between the external pair of on-site potential and site-dependent hopping and the internal pair of density and kinetic-energy density. Based on this mapping we establish two unknown effective fields, the mean-field exchange-correlation potential and the mean-field exchange-correlation hopping, that force the keKS system to generate the same kinetic-energy density and density as the fully interacting one. We show, by a decomposition based on the equations of motions for the density and the kinetic-energy density, that we can construct simple orbital-dependent functionals that outperform the corresponding exact-exchange Kohn-Sham (KS) approximation of standard density-functional theory. We do so by considering the exact KS and keKS systems and compare the unknown correlation contributions as well as by comparing self-consistent calculations based on the mean-field exchange for the keKS and the exact-exchange for the KS system, respectively.

References in corpus (32)

• Perspective on density functional theory
• Structure of Fermionic Density Matrices: Complete N-representability Conditions
• Quantum marginal problem and N-representability
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Mapping from current densities to vector potentials in time-dependent current-density functional theory
• Density functional theory for strongly interacting electrons
• The Hubbard Dimer: A density functional case study of a many-body problem
• Numerical Methods for the Inverse Problem of Density Functional Theory
• Reduction of Electronic Wavefunctions to Kohn-Sham Effective Potentials
• Quantum many-body dynamics in a Lagrangian frame: II. Geometric formulation of time-dependent density functional theory
• Differentiable but exact formulation of density-functional theory
• Density-functional theory and the v-representability problem for model strongly correlated electron systems
• Time-dependent current density functional theory on a lattice
• Generalized Pauli constraints in reduced density matrix functional theory
• Existence, Uniqueness, and Construction of the Density-Potential Mapping in Time-Dependent Density-Functional Theory
• Density-Matrix functional theory of strongly-correlated lattice fermions
• Local Control and v-Representability of Correlated Quantum Dynamics
• Landscape of an exact energy functional
• Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations
• Derivative discontinuity and exchange-correlation potential of meta-GGAs in density-functional theory
• Exchange-correlation functionals from the strongly-interacting limit of DFT: Applications to model chemical systems
• Reduced density-matrix functionals applied to the Hubbard dimer
• Density-Functional Theory of Thermoelectric Phenomena
• Time-Dependent Density Functional Theory Beyond Kohn-Sham Slater Determinants
• No-go theorem for the description of Mott phenomena with conventional Density Functional Theory methods
• Exact functionals for correlated electron-photon systems
• Taming Density Functional Theory by Coarse-Graining
• Exact Maps in Density Functional Theory for Lattice Models
• Functional theories of thermoelectric phenomena
• Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms
• Orbitals from local RDMFT: Are they Kohn-Sham or Natural Orbitals?
• Structure of the first order Reduced Density Matrix in three electron systems: A Generalized Pauli Constraints assisted study

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• Local and global interpolations along the adiabatic connection of DFT: A study at different correlation regimes
• Partially deorbitalized meta-GGA
• Off-shell effective energy theory: a unified treatment of the Hubbard model from d=1 to d=$\infty$
• Many Electrons and the Photon Field -- The many-body structure of nonrelativistic quantum electrodynamics
• Comparing correlation components and approximations in Hartree-Fock and Kohn-Sham theories via an analytical test case study