No-go theorem for the description of Mott phenomena with conventional Density Functional Theory methods

Abstract

Density functional theory provides the most widespread framework for the realistic description of the electronic structure of solids, but the description of strongly-correlated systems has remained so far elusive. Here we consider a particular limit of electrons in a periodic ionic potential in which a one-band description becomes exact all the way from the weakly-correlated metallic regime to the strongly-correlated Mott-Hubbard regime. We provide a necessary condition a density functional should fulfill to describe Mott-Hubbard behavior and show that it is not satisfied by standard and widely used local, semilocal and hybrid functionals. We illustrate the condition in the case of a few-atom system and provide an analytic approximation to the exact exchange-correlation potential based on a variational wave function which shows explicitly the correct behavior providing a robust scheme to combine lattice and continuum methods.

29 pages, 8 figures

References in corpus (8)

• Gutzwiller density functional theory for correlated electron systems
• Electron spectra close to a metal-to-insulator transition
• Kohn-Sham Kinetic Energy Density in the Nuclear and Asymptotic Regions: Deviations from the Von Weizsäcker Behavior and Applications to Density Functionals
• Relevance of coordinate and particle-number scaling in density functional theory
• Semilocal density functional theory with correct surface asymptotics
• Phase Diagram of Na${}_x$CoO${}_2$ Studied by Gutzwiller Density Functional Theory
• The Mott insulator - 10th order perturbation theory extended to infinite order using QMC
• Ground state of the frustrated Hubbard model within DMFT: energetics of Mott insulator and metal from ePT and QMC

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• Functional Derivative of the Zero Point Energy Functional from the Strong Interaction Limit of Density Functional Theory
• Sum-rules of the response potential in the strongly-interacting limit of DFT
• Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer
• Kinetic correlation functionals from the entropic regularisation of the strictly-correlated electrons problem
• Comparing correlation components and approximations in Hartree-Fock and Kohn-Sham theories via an analytical test case study
• Strong parameter renormalization from optimum lattice model orbitals