Impurity and boundary effects in one and two-dimensional inhomogeneous Heisenberg antiferromagnets

We calculate the ground-state energy of one and two-dimensional spatially inhomogeneous antiferromagnetic Heisenberg models for spins 1/2, 1, 3/2 and 2. Our calculations become possible as a consequence of the recent formulation of density-functional theory for Heisenberg models. The method is similar to spin-density-functional theory, but employs a local-density-type approximation designed specifically for the Heisenberg model, allowing us to explore parameter regimes that are hard to access by traditional methods, and to consider complications that are important specifically for nanomagnetic devices, such as the effects of impurities, finite-size, and boundary geometry, in chains, ladders, and higher-dimensional systems.Comment: 4 pages, 4 figures, accepted by Phys. Rev.

How tight is the Lieb-Oxford bound?

Density-functional theory requires ever better exchange-correlation (xc) functionals for the ever more precise description of many-body effects on electronic structure. Universal constraints on the xc energy are important ingredients in the construction of improved functionals. Here we investigate one such universal property of xc functionals: the Lieb-Oxford lower bound on the exchange-correlation energy, $E_{xc}[n] \ge -C \int d^3r n^{4/3}$, where $C\leq C_{LO}=1.68$. To this end, we perform a survey of available exact or near-exact data on xc energies of atoms, ions, molecules, solids, and some model Hamiltonians (the electron liquid, Hooke's atom and the Hubbard model). All physically realistic density distributions investigated are consistent with the tighter limit $C \leq 1$. For large classes of systems one can obtain class-specific (but not fully universal) similar bounds. The Lieb-Oxford bound with $C_{LO}=1.68$ is a key ingredient in the construction of modern xc functionals, and a substantial change in the prefactor $C$ will have consequences for the performance of these functionals.Comment: 10 pages, 3 figure

Effects of nanoscale spatial inhomogeneity in strongly correlated systems

We calculate ground-state energies and density distributions of Hubbard superlattices characterized by periodic modulations of the on-site interaction and the on-site potential. Both density-matrix renormalization group and density-functional methods are employed and compared. We find that small variations in the on-site potential $v_i$ can simulate, cancel, or even overcompensate effects due to much larger variations in the on-site interaction $U_i$. Our findings highlight the importance of nanoscale spatial inhomogeneity in strongly correlated systems, and call for reexamination of model calculations assuming spatial homogeneity.Comment: 5 pages, 1 table, 4 figures, to appear in PR

Non-empirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound

A simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation leads to an alternative point of view on popular hybrid functionals, providing a rationale for why they work and how they can be constructed. A similar representation of the exact correlation functional allows to construct fully non-empirical hyper-generalized-gradient approximations (HGGAs), radically departing from established paradigms of functional construction. Numerical tests of these HGGAs for atomic and molecular correlation energies and molecular atomization energies show that even simple HGGAs match or outperform state-of-the-art correlation functionals currently used in solid-state physics and quantum chemistry.Comment: v2: Major revison. Added information on relation to the gradient expansion and to local hybrids, improved discussion of size consistency and of performance relative to other functional

Dimensional-scaling estimate of the energy of a large system from that of its building blocks: Hubbard model and Fermi liquid

A simple, physically motivated, scaling hypothesis, which becomes exact in important limits, yields estimates for the ground-state energy of large, composed, systems in terms of the ground-state energy of its building blocks. The concept is illustrated for the electron liquid, and the Hubbard model. By means of this scaling argument the energy of the one-dimensional half-filled Hubbard model is estimated from that of a 2-site Hubbard dimer, obtaining quantitative agreement with the exact one-dimensional Bethe-Ansatz solution, and the energies of the two- and three-dimensional half-filled Hubbard models are estimated from the one-dimensional energy, recovering exact results for $U\to 0$ and $U\to \infty$ and coming close to Quantum Monte Carlo data for intermediate $U$.Comment: 3 figure

BCS and generalized BCS superconductivity in relativistic quantum field theory. I. formulation

We investigate the BCS and generalized BCS theories in the relativistic quantum field theory. We select the gauge freedom as U(1), and introduce a BCS-type effective attractive interaction. After introducing the Gor'kov formalism and performing the group theoretical consideration of the mean fields, we solve the relativistic Gor'kov equation and obtain the Green's functions in analytical forms. We obtain various types of gap equations.Comment: 31 page

The entanglement of few-particle systems when using the local-density approximation

In this chapter we discuss methods to calculate the entanglement of a system using density-functional theory. We firstly introduce density-functional theory and the local-density approximation (LDA). We then discuss the concept of the `interacting LDA system'. This is characterised by an interacting many-body Hamiltonian which reproduces, uniquely and exactly, the ground state density obtained from the single-particle Kohn-Sham equations of density-functional theory when the local-density approximation is used. We motivate why this idea can be useful for appraising the local-density approximation in many-body physics particularly with regards to entanglement and related quantum information applications. Using an iterative scheme, we find the Hamiltonian characterising the interacting LDA system in relation to the test systems of Hooke's atom and helium-like atoms. The interacting LDA system ground state wavefunction is then used to calculate the spatial entanglement and the results are compared and contrasted with the exact entanglement for the two test systems. For Hooke's atom we also compare the entanglement to our previous estimates of an LDA entanglement. These were obtained using a combination of evolutionary algorithm and gradient descent, and using an LDA-based perturbative approach. We finally discuss if the position-space information entropy of the density---which can be obtained directly from the system density and hence easily from density-functional theory methods---can be considered as a proxy measure for the spatial entanglement for the test systems.Comment: 12 pages and 5 figures

Density-functional calculation of ionization energies of current-carrying atomic states

Current-density-functional theory is used to calculate ionization energies of current-carrying atomic states. A perturbative approximation to full current-density-functional theory is implemented for the first time, and found to be numerically feasible. Different parametrizations for the current-dependence of the density functional are critically compared. Orbital currents in open-shell atoms turn out to produce a small shift in the ionization energies. We find that modern density functionals have reached an accuracy at which small current-related terms appearing in open-shell configurations are not negligible anymore compared to the remaining difference to experiment.Comment: 7 pages, 2 tables, accepted by Phys. Rev.