Exact exchange-correlation potential of an ionic Hubbard model with a free surface

Nonadiabatic Exchange-Correlation Potential for Strongly Correlated Materials in the Weak and Strong Interaction Limits

In this work, nonadiabatic exchange-correlation (XC) potentials for time-dependent density-functional theory (TDDFT) for strongly correlated materials are derived in the limits of strong and weak correlations. After summarizing some essentials of the available dynamical mean-field theory (DMFT) XC potentials valid for these systems, we present details of the Sham–Schluter equation approach that we use to obtain, in principle, an exact XC potential from a many-body theory solution for the nonequilibrium electron self-energy. We derive the XC potentials for the one-band Hubbard model in the limits of weak and strong on-site Coulomb repulsion. To test the accuracy of the obtained potentials, we compare the TDDFT results obtained with these potentials with the corresponding nonequilibrium DMFT solution for the one-band Hubbard model and find that the agreement between the solutions is rather good. We also discuss possible directions to obtain a universal XC potential that would be appropriate for the case of intermediate interaction strengths, i.e., a nonadiabatic potential that can be used to perform TDDFT analysis of nonequilibrium phenomena, such as transport and other ultrafast properties of materials with any strength of electron correlation at any value in the applied perturbing field.

Mott Metal-Insulator Transition from Steady-State Density Functional Theory

We present a computationally efficient method to obtain the spectral function of bulk systems in the framework of steady-state density functional theory (i-DFT) using an idealized scanning tunneling microscope (STM) setup. We calculate the current through the STM tip and then extract the spectral function from the finite-bias differential conductance. The fictitious noninteracting system of i-DFT features an exchange-correlation (XC) contribution to the bias which guarantees the same current as in the true interacting system. Exact properties of the XC bias are established using Fermi-liquid theory and subsequently implemented to construct approximations for the Hubbard model. We show for two different lattice structures that the Mott metal-insulator transition is captured by i-DFT.

Recent Progress in Lattice Density Functional Theory

Recent developments in the density-functional theory of electron correlations in many-body lattice models are reviewed. The theoretical framework of lattice density-functional theory (LDFT) is briefly recalled, giving emphasis to its universality and to the central role played by the single-particle density-matrix γ . The Hubbard model and the Anderson single-impurity model are considered as relevant explicit problems for the applications. Real-space and reciprocal-space approximations to the fundamental interaction-energy functional W [ γ ] are introduced, in the framework of which the most important ground-state properties are derived. The predictions of LDFT are contrasted with available exact analytical results and state-of-the-art numerical calculations. Thus, the goals and limitations of the method are discussed.

Testing Exact Upper Bounds to Exact Exchange

The exact exchange energy and its energy density are useful but computationally expensive ingredients in density functional approximations for Kohn-Sham density functional theory. We present detailed tests of some exact nonempirical upper bounds to exact exchange. These "Rung 3.5" upper bounds contract the Kohn-Sham one-particle density matrix with model density matrices used to construct semilocal model exchange holes and invoke the Cauchy-Schwarz inequality. The contraction automatically eliminates the computationally expensive long-range component of the exact exchange hole. Numerical tests show that the exchange upper bounds underestimate total exchange energies while predicting other properties with accuracy approaching standard hybrid approximations.

From the Kohn–Sham band gap to the fundamental gap in solids. An integer electron approach

The upshift Δ of the level at the bottom of the conduction band (the LUMO) from the neutral N-electron crystal to the negative N + 1 system, and therefore the fundamental gap ε_LUMO(N + 1) − ε_HOMO(N) = I − A, can be calculated simply and cheaply from the response part of v_xc.

Derivative discontinuity in the strong-interaction limit of density-functional theory

We generalize the exact strong-interaction limit of the exchange-correlation energy of Kohn-Sham density functional theory to open systems with fluctuating particle numbers. When used in the self-consistent Kohn-Sham procedure on strongly interacting systems, this functional yields exact features crucial for important applications such as quantum transport. In particular, the steplike structure of the highest-occupied Kohn-Sham eigenvalue is very well captured, with accurate quantitative agreement with exact many-body chemical potentials. While it can be shown that a sharp derivative discontinuity is present only in the infinitely strongly correlated limit, at finite correlation regimes we observe a slightly smoothened discontinuity, with qualitative and quantitative features that improve with increasing correlation. From the fundamental point of view, our results obtain the derivative discontinuity without making the assumptions used in its standard derivation, offering independent support for its existence.