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The celebrated antiferromagnetic phase transition was realized in a most recent optical lattice experiment for 3D fermionic Hubbard model [Shao {\it et al}., Nature {\bf 632}, 267 (2024)]. Despite the great achievement, it was observed that…
Physical properties of the quantum gravitational vacuum state are explored by solving a lattice version of the Wheeler-DeWitt equation. The constraint of diffeomorphism invariance is strong enough to uniquely determine the structure of the…
The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U) were determined for an infinite atomic chain. In effect, the electronic properties of the chain as a function of interatomic distance R…
We formulate a set of equations that facilitate an exact numerical solution of the Kohn-Sham potential for a finite Hubbard chain with nearest neighbour hopping and arbitrary site potentials. The approach relies on a mapping of the…
We generalize the dynamical - mean field theory (DMFT) by including into the DMFT equations dependence on correlation length of pseudogap fluctuations via additional (momentum dependent) self - energy. This self - energy describes non -…
Local density approximation (LDA) to the density functional theory (DFT) has continuous derivative of total energy as a number of electrons function and continuous exchange-correlation potential, while in exact DFT both should be…
We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity…
Properties of hcp-Ti such as elastic constants, stacking faults and gamma-surfaces are computed using Density Functional Theory (DFT) and two central force Embedded Atom interaction Models (EAM). The results are compared to previously…
Density matrix embedding theory (DMET) provides a framework to describe ground-state expectation values in strongly correlated systems, but its extension to dynamical quantities is still an open problem. We show one route to obtaining…
Reporting extensions of a recently developed approach to density functional theory with correct long-range be-havior (Phys. Rev. Lett. 94, 043002 (2005)). The central quantities are a splitting functional gamma[n] and a complementary…
The ground states of the two-dimensional repulsive Hubbard model are studied within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge properties are determined by systematic, large-scale, exact numerical calculations, and…
We propose and work out a reduced density matrix functional theory (RDMFT) for calculating energies of eigenstates of interacting many-electron systems beyond the ground state. Various obstacles which historically have doomed such an…
In electronic structure methods based on the correction of approximate density-functional theory (DFT) for systematic inaccuracies, Hubbard $U$ parameters may be used to quantify and amend the self-interaction errors ascribed to selected…
It is shown that a minimum realization of the dynamical mean-field theory (DMFT) can be achieved by mapping a correlated lattice model onto an impurity model in which the impurity is coupled to an uncorrelated bath that consists of a single…
We describe a recent implementation of the combined GW and dynamical mean field (DMFT) method "GW+DMFT" for the two-dimensional Hubbard model with on-site and nearest-neighbor repulsion. We clarify the relation of the GW+DMFT scheme to…
We illustrate the scope of Time Dependent Density Functional Theory (TDDFT) for strongly correlated (lattice) models out of equilibrium. Using the exact many body time evolution, we reverse engineer the exact exchange correlation (xc)…
Density functional theory (DFT) has greatly expanded our ability to affordably compute and understand electronic ground states, by replacing intractable {\em ab initio} calculations by models based on paradigmatic physics from high- and…
An overarching question in strongly correlated electron systems is how the landscape of quantum phases emerges from electron correlations. The method of extended dynamical mean field theory (EDMFT) has been developed for clean lattice…
We realize and study the ionic Hubbard model using an interacting two-component gas of fermionic atoms loaded into an optical lattice. The bipartite lattice has honeycomb geometry with a staggered energy-offset that explicitly breaks the…
We provide solid evidence for the long-standing presumption that model Hamiltonians with short-range interactions faithfully reproduce the physics of the long-range Coulomb interaction in real materials. For this aim, we address a generic…