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.

Bosonization solution of the Falicov-Kimball model

We use a novel approach to analyze the one dimensional spinless Falicov-Kimball model. We derive a simple effective model for the occupation of the localized orbitals which clearly reveals the origin of the known ordering. Our study is extended to a quantum model with hybridization between the localized and itinerant states; we find a crossover between the well-known weak- and strong-coupling behaviour. The existence of electronic polarons at intermediate coupling is confirmed. A phase diagram is presented and discussed in detail.Comment: RevTex, 10 pages, 1 figur

Comment on "Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains"

Dukelsky, Mart\'in-Delgado, Nishino and Sierra (Europhys. Lett., 43, 457 (1998) - hereafter referred to as DMNS) investigated the matrix product method (MPM), comparing it with the infinite-size density matrix renormalization group (DMRG). For equivalent basis size, the MPM produces an improved variational energy over that produced by DMRG and, unlike DMRG, produces a translationally-invariant wavefunction. The DMRG results presented were significantly worse than the MPM, caused by a shallow bound state appearing at the join of the two DMRG blocks. They also suggested that the DMRG results can be improved by using an alternate superblock construction $[B] \bullet [B]$ for the last few steps of the calculation. In this comment, we show that the DMRG results presented by DMNS are in error and the artificial bound state produced by the standard superblock configuration is very small even for $m=2$ states kept. In addition, we calculate explicitly the energy and wavefunction for the $[B] \bullet [B]$ superblock structure and verify that the energy coincides with that of the MPM, as conjectured by S. Ostlund and S. Rommer (Phys. Rev. Lett., 75, 3537 (1995)).Comment: 2 pages, 1 eps figure included. eps.cls include

Electronic polarons in an extended Falicov-Kimball model

We examine the one-dimensional spinless Falicov-Kimball model extended by a hybridization potential between the localized and itinerant electron states. Below half-filling we find a crossover from a mixed-valence metal to an integer-valence phase separated state with increasing on-site Coulomb repulsion. This crossover regime is characterized by local competition between the strong- and weak-coupling behaviour, manifested by the formation of an electronic polaron liquid. We identify this intermediate-coupling regime as a charge-analogy of the Griffiths phase; a phase diagram is presented and discussed in detail.Comment: RevTex, 10 pages, 1 figure; revised discussio

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

Competing Orderings in an Extended Falicov-Kimball Model

We present a Hartree-Fock study of the Falicov-Kimball model extended by both on-site and non-local hybridization. We examine the interplay between excitonic effects and the charge-density wave (CDW) instability known to exist at zero hybridization. It is found that the CDW state remains stable in the presence of finite hybridization; for on-site hybridization the Coulomb interaction nevertheless strongly enhances the excitonic average above its value in the noninteracting system. In contrast, for non-local hybridization, we observe no such enhancement of the excitonic average or a spontaneous on-site hybridization potential. Instead, we find only a significant suppression of the excitonic correlations in the CDW state. A phenomenological Ginzburg-Landau analysis is also provided to understand the interplay.Comment: RevTex, 5 pages, 4 figures; expanded and corrected, typos added, references adde

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 Ground States of the Periodic Anderson Model in D=3 Dimensions

We construct a class of exact ground states of three-dimensional periodic Anderson models (PAMs) -- including the conventional PAM -- on regular Bravais lattices at and above 3/4 filling, and discuss their physical properties. In general, the f electrons can have a (weak) dispersion, and the hopping and the non-local hybridization of the d and f electrons extend over the unit cell. The construction is performed in two steps. First the Hamiltonian is cast into positive semi-definite form using composite operators in combination with coupled non-linear matching conditions. This may be achieved in several ways, thus leading to solutions in different regions of the phase diagram. In a second step, a non-local product wave function in position space is constructed which allows one to identify various stability regions corresponding to insulating and conducting states. The compressibility of the insulating state is shown to diverge at the boundary of its stability regime. The metallic phase is a non-Fermi liquid with one dispersing and one flat band. This state is also an exact ground state of the conventional PAM and has the following properties: (i) it is non-magnetic with spin-spin correlations disappearing in the thermodynamic limit, (ii) density-density correlations are short-ranged, and (iii) the momentum distributions of the interacting electrons are analytic functions, i.e., have no discontinuities even in their derivatives. The stability regions of the ground states extend through a large region of parameter space, e.g., from weak to strong on-site interaction U. Exact itinerant, ferromagnetic ground states are found at and below 1/4 filling.Comment: 47 pages, 10 eps 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

Electron spin resonance signal of Luttinger liquids and single-wall carbon nanotubes

A comprehensive theory of electron spin resonance (ESR) for a Luttinger liquid (LL) state of correlated metals is presented. The ESR measurables such as the signal intensity and the line-width are calculated in the framework of Luttinger liquid theory with broken spin rotational symmetry as a function of magnetic field and temperature. We obtain a significant temperature dependent homogeneous line-broadening which is related to the spin symmetry breaking and the electron-electron interaction. The result crosses over smoothly to the ESR of itinerant electrons in the non-interacting limit. These findings explain the absence of the long-sought ESR signal of itinerant electrons in single-wall carbon nanotubes when considering realistic experimental conditions.Comment: 5 pages, 1 figur