Stability of Ferromagnetism in Hubbard models with degenerate single-particle ground states

A Hubbard model with a N_d-fold degenerate single-particle ground state has ferromagnetic ground states if the number of electrons is less or equal to N_d. It is shown rigorously that the local stability of ferromagnetism in such a model implies global stability: The model has only ferromagnetic ground states, if there are no single spin-flip ground states. If the number of electrons is equal to N_d, it is well known that the ferromagnetic ground state is unique if and only if the single-particle density matrix is irreducible. We present a simplified proof for this result.Comment: accepted for publication in J. Phys.

Theory of the Anderson impurity model: The Schrieffer--Wolff transformation re--examined

We apply the method of infinitesimal unitary transformations recently introduced by Wegner to the Anderson single impurity model. It is demonstrated that this method provides a good approximation scheme for all values of the on-site interaction $U$, it becomes exact for $U=0$. We are able to treat an arbitrary density of states, the only restriction being that the hybridization should not be the largest parameter in the system. Our approach constitutes a consistent framework to derive various results usually obtained by either perturbative renormalization in an expansion in the hybridization~$\Gamma$, Anderson's ``poor man's" scaling approach or the Schrieffer--Wolff unitary transformation. In contrast to the Schrieffer--Wolff result we find the correct high--energy cutoff and avoid singularities in the induced couplings. An important characteristic of our method as compared to the ``poor man's" scaling approach is that we continuously decouple modes from the impurity that have a large energy difference from the impurity orbital energies. In the usual scaling approach this criterion is provided by the energy difference from the Fermi surface.Comment: Uuencoded gzipped postscript, 26 pages, 5 postscript figure

Ferromagnetism in a Hubbard model for an atomic quantum wire: a realization of flat-band magnetism from even-membered rings

We have examined a Hubbard model on a chain of squares, which was proposed by Yajima et al as a model of an atomic quantum wire As/Si(100), to show that the flat-band ferromagnetism according to a kind of Mielke-Tasaki mechanism should be realized for an appropriate band filling in such a non-frustrated lattice. Reflecting the fact that the flat band is not a bottom one, the ferromagnetism vanishes, rather than intensified, as the Hubbard U is increased. The exact diagonalization method is used to show that the critical value of U is in a realistic range. We also discussed the robustness of the magnetism against the degradation of the flatness of the band.Comment: misleading terms and expressions are corrected, 4 pages, RevTex, 5 figures in Postscript, to be published in Phys. Rev. B (rapid communication

Relationship between spiral and ferromagnetic states in the Hubbard model in the thermodynamic limit

We explore how the spiral spin(SP) state, a spin singlet known to accompany fully-polarized ferromagnetic (F) states in the Hubbard model, is related with the F state in the thermodynamic limit using the density matrix renormalization group and exact diagonalization. We first obtain an indication that when the F state is the ground state the SP state is also eligible as the ground state in that limit. We then follow the general argument by Koma and Tasaki [J. Stat. Phys. {\bf 76}, 745 (1994)] to find that: (i) The SP state possesses a kind of order parameter. (ii) Although the SP state does not break the SU(2) symmetry in finite systems, it does so in the thermodynamic limit by making a linear combination with other states that are degenerate in that limit. We also calculate the one-particle spectral function and dynamical spin and charge susceptibilities for various 1D finite-size lattices. We find that the excitation spectrum of the SP state and the F state is almost identical. Our present results suggest that the SP and the F states are equivalent in the thermodynamic limit. These properties may be exploited to determine the magnetic phase diagram from finite-size studies.Comment: 17 figures, to be published in Phys. Rev.

Flat-Bands on Partial Line Graphs -- Systematic Method for Generating Flat-Band Lattice Structures

We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied to two- and three-dimensional systems. We show examples of partial line graphs of square and cubic lattices. The method is useful in providing a guideline for synthesizing materials with flat energy bands, since the tight-binding models on the partial line graphs provide us a large room for modification, maintaining the flat energy dispersions.Comment: 9 pages, 4 figure

Flat-band ferromagnetism induced by off-site repulsions

Density matrix renormalization group method is used to analyze how the nearest-neighbor repulsion V added to the Hubbard model on 1D triangular lattice and a railway trestle (t-t') model will affect the electron-correlation dominated ferromagnetism arising from the interference (frustration). Obtained phase diagram shows that there is a region in smaller-t' side where the critical on-site repulsion above which the system becomes ferromagnetic is reduced when the off-site repulsion is introduced.Comment: 4 pages, RevTex, 6 figures in Postscript, to be published in Phys. Rev.

Effective rate equations for the over-damped motion in fluctuating potentials

We discuss physical and mathematical aspects of the over-damped motion of a Brownian particle in fluctuating potentials. It is shown that such a system can be described quantitatively by fluctuating rates if the potential fluctuations are slow compared to relaxation within the minima of the potential, and if the position of the minima does not fluctuate. Effective rates can be calculated; they describe the long-time dynamics of the system. Furthermore, we show the existence of a stationary solution of the Fokker-Planck equation that describes the motion within the fluctuating potential under some general conditions. We also show that a stationary solution of the rate equations with fluctuating rates exists.Comment: 18 pages, 2 figures, standard LaTeX2

Optical excitations in hexagonal nanonetwork materials

Optical excitations in hexagonal nanonetwork materials, for example, Boron-Nitride (BN) sheets and nanotubes, are investigated theoretically. The bonding of BN systems is positively polarized at the B site, and is negatively polarized at the N site. There is a permanent electric dipole moment along the BN bond, whose direction is from the B site to the N site. When the exciton hopping integral is restricted to the nearest neighbors, the flat band of the exciton appears at the lowest energy. The higher optical excitations have excitation bands similar to the electronic bands of graphene planes and carbon nanotubes. The symmetry of the flat exciton band is optically forbidden, indicating that the excitons related to this band will show quite long lifetime which will cause strong luminescence properties.Comment: 4 pages; 3 figures; proceedings of "XVIth International Winterschool on Electronic Properties of Novel Materials (IWEPNM2002)

Temperature in One-Dimensional Bosonic Mott insulators

The Mott insulating phase of a one-dimensional bosonic gas trapped in optical lattices is described by a Bose-Hubbard model. A continuous unitary transformation is used to map this model onto an effective model conserving the number of elementary excitations. We obtain quantitative results for the kinetics and for the spectral weights of the low-energy excitations for a broad range of parameters in the insulating phase. By these results, recent Bragg spectroscopy experiments are explained. Evidence for a significant temperature of the order of the microscopic energy scales is found.Comment: 8 pages, 7 figure