Ferromagnetism without flat bands in thin armchair nanoribbons

Describing by a Hubbard type of model a thin armchair graphene ribbon in the armchair hexagon chain limit, one shows in exact terms, that even if the system does not have flat bands at all, at low concentration a mesoscopic sample can have ferromagnetic ground state, being metallic in the same time. The mechanism is connected to a common effect of correlations and confinement.Comment: 37 pages, 12 figures, in press at Eur. Phys. Jour.

Exact ground states for the four-electron problem in a Hubbard ladder

The exact ground state of four electrons in an arbitrary large two leg Hubbard ladder is deduced from nine analytic and explicit linear equations. The used procedure is described, and the properties of the ground state are analyzed. The method is based on the construction in r-space of the different type of orthogonal basis wave vectors which span the subspace of the Hilbert space containing the ground state. In order to do this, we start from the possible microconfigurations of the four particles within the system. These microconfigurations are then rotated, translated and spin-reversed in order to build up the basis vectors of the problem. A closed system of nine analytic linear equations is obtained whose secular equation, by its minimum energy solution, provides the ground state energy and the ground state wave function of the model.Comment: 10 pages, 7 figure

Charge Order in the Falicov-Kimball Model

We examine the spinless one-dimensional Falicov-Kimball model (FKM) below half-filling, addressing both the binary alloy and valence transition interpretations of the model. Using a non-perturbative technique, we derive an effective Hamiltonian for the occupation of the localized orbitals, providing a comprehensive description of charge order in the FKM. In particular, we uncover the contradictory ordering roles of the forward-scattering and backscattering itinerant electrons: the latter are responsible for the crystalline phases, while the former produces the phase separation. We find an Ising model describes the transition between the phase separated state and the crystalline phases; for weak-coupling we present the critical line equation, finding excellent agreement with numerical results. We consider several extensions of the FKM that preserve the classical nature of the localized states. We also investigate a parallel between the FKM and the Kondo lattice model, suggesting a close relationship based upon the similar orthogonality catastrophe physics of the associated single-impurity models.Comment: 39 pages, 6 figure

Exact analytic results for the Gutzwiller wave function with finite magnetization

We present analytic results for ground-state properties of Hubbard-type models in terms of the Gutzwiller variational wave function with non-zero values of the magnetization m. In dimension D=1 approximation-free evaluations are made possible by appropriate canonical transformations and an analysis of Umklapp processes. We calculate the double occupation and the momentum distribution, as well as its discontinuity at the Fermi surface, for arbitrary values of the interaction parameter g, density n, and magnetization m. These quantities determine the expectation value of the one-dimensional Hubbard Hamiltonian for any symmetric, monotonically increasing dispersion epsilon_k. In particular for nearest-neighbor hopping and densities away from half filling the Gutzwiller wave function is found to predict ferromagnetic behavior for sufficiently large interaction U.Comment: REVTeX 4, 32 pages, 8 figure

Extended DFT+U+V method with on-site and inter-site electronic interactions

In this article we introduce a generalization of the popular DFT+U method based on the extended Hubbard model that includes on-site and inter-site electronic interactions. The novel corrective Hamiltonian is designed to study systems for which electrons are not completely localized on atomic states (according to the general scheme of Mott localization) and hybridization between orbitals from different sites plays an important role. The application of the extended functional to archetypal Mott - charge-transfer (NiO) and covalently bonded insulators (Si and GaAs) demonstrates its accuracy and versatility and the possibility to obtain a unifying and equally accurate description for a broad range of very diverse systems

Four electrons in a two-leg Hubbard ladder: exact ground states

In the case of a two-leg Hubbard ladder we present a procedure which allows the exact deduction of the ground state for the four particle problem in arbitrary large lattice system, in a tractable manner, which involves only a reduced Hilbert space region containing the ground state. In the presented case, the method leads to nine analytic, linear, and coupled equations providing the ground state. The procedure which is applicable to few particle problems and other systems as well is based on an r-space representation of the wave functions and construction of symmetry adapted orthogonal basis wave vectors describing the Hilbert space region containing the ground state. Once the ground state is deduced, a complete quantum mechanical characterization of the studied state can be given. Since the analytic structure of the ground state becomes visible during the use of the method, its importance is not reduced only to the understanding of theoretical aspects connected to exact descriptions or potential numerical approximation scheme developments, but is relevant as well for a large number of potential technological application possibilities placed between nano-devices and quantum calculations, where the few particle behavior and deep understanding are important key aspects to know.Comment: 19 pages, 5 figure

Finite size scaling in the 2D XY-model and generalized universality

In recent works (BHP), a generalized universality has been proposed, linking phenomena as dissimilar as 2D magnetism and turbulence. To test these ideas, we performed a MC study of the 2D XY-model. We found that the shape of the probability distribution function for the magnetization M is non Gaussian and independent of the system size --in the range of the lattice sizes studied-- below the Kosterlitz-Thoules temperature. However, the shape of these distributions does depend on the temperature, contrarily to the BHP's claim. This behavior is successfully explained by using an extended finite-size scaling analysis and the existence of bounds for M.Comment: 7 pages, 5 figures. Submitted to Phys. Rev. Lett. Details of changes: 1. We emphasized in the abstract the range of validity of our results. 2. In the last paragraph the temperature dependence of the PDF was slightly re-formulate

Exact ground states for the four-electron problem in a two-dimensional finite Hubbard square system

We present exact explicit analytical results describing the exact ground state of four electrons in a two dimensional square Hubbard cluster containing 16 sites taken with periodic boundary conditions. The presented procedure, which works for arbitrary even particle number and lattice sites, is based on explicitly given symmetry adapted base vectors constructed in r-space. The Hamiltonian acting on these states generates a closed system of 85 linear equations providing by its minimum eigenvalue the exact ground state of the system. The presented results, described with the aim to generate further creative developments, not only show how the ground state can be exactly obtained and what kind of contributions enter in its construction, but emphasize further characteristics of the spectrum. On this line i) possible explications are found regarding why weak coupling expansions often provide a good approximation for the Hubbard model at intermediate couplings, or ii) explicitly given low lying energy states of the kinetic energy, avoiding double occupancy, suggest new roots for pairing mechanism attracting decrease in the kinetic energy, as emphasized by kinetic energy driven superconductivity theories.Comment: 37 pages, 18 figure