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

Antiferromagnetism in the Exact Ground State of the Half Filled Hubbard Model on the Complete-Bipartite Graph

As a prototype model of antiferromagnetism, we propose a repulsive Hubbard Hamiltonian defined on a graph \L={\cal A}\cup{\cal B} with ${\cal A}\cap {\cal B}=\emptyset$ and bonds connecting any element of ${\cal A}$ with all the elements of ${\cal B}$. Since all the hopping matrix elements associated with each bond are equal, the model is invariant under an arbitrary permutation of the ${\cal A}$-sites and/or of the ${\cal B}$-sites. This is the Hubbard model defined on the so called $(N_{A},N_{B})$-complete-bipartite graph, $N_{A}$ ($N_{B}$) being the number of elements in ${\cal A}$ (${\cal B}$). In this paper we analytically find the {\it exact} ground state for $N_{A}=N_{B}=N$ at half filling for any $N$; the repulsion has a maximum at a critical $N$-dependent value of the on-site Hubbard $U$. The wave function and the energy of the unique, singlet ground state assume a particularly elegant form for N \ra \inf. We also calculate the spin-spin correlation function and show that the ground state exhibits an antiferromagnetic order for any non-zero $U$ even in the thermodynamic limit. We are aware of no previous explicit analytic example of an antiferromagnetic ground state in a Hubbard-like model of itinerant electrons. The kinetic term induces non-trivial correlations among the particles and an antiparallel spin configuration in the two sublattices comes to be energetically favoured at zero Temperature. On the other hand, if the thermodynamic limit is taken and then zero Temperature is approached, a paramagnetic behavior results. The thermodynamic limit does not commute with the zero-Temperature limit, and this fact can be made explicit by the analytic solutions.Comment: 19 pages, 5 figures .ep

Design of multivariable feedback control systems via spectral assignment

The applicability of spectral assignment techniques to the design of multivariable feedback control systems was investigated. A fractional representation design procedure for unstable plants is presented and illustrated with an example. A computer aided design software package implementing eigenvalue/eigenvector design procedures is described. A design example which illustrates the use of the program is explained

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.

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

Modulation Equations: Stochastic Bifurcation in Large Domains

We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic Ginzburg-Landau equation. We then proceed to show that this approximation also extends to the invariant measures of these equations

Asymptotic dynamics in 3D gravity with torsion

We study the nature of boundary dynamics in the teleparallel 3D gravity. The asymptotic field equations with anti-de Sitter boundary conditions yield only two non-trivial boundary modes, related to a conformal field theory with classical central charge. After showing that the teleparallel gravity can be formulated as a Chern-Simons theory, we identify dynamical structure at the boundary as the Liouville theory.Comment: 16 pages, RevTeX, no figure

Calculating critical temperatures of superconductivity from a renormalized Hamiltonian

It is shown that one can obtain quantitatively accurate values for the superconducting critical temperature within a Hamiltonian framework. This is possible if one uses a renormalized Hamiltonian that contains an attractive electron-electron interaction and renormalized single particle energies. It can be obtained by similarity renormalization or using flow equations for Hamiltonians. We calculate the critical temperature as a function of the coupling using the standard BCS-theory. For small coupling we rederive the McMillan formula for Tc. We compare our results with Eliashberg theory and with experimental data from various materials. The theoretical results agree with the experimental data within 10%. Renormalization theory of Hamiltonians provides a promising way to investigate electron-phonon interactions in strongly correlated systems.Comment: 6 pages, LaTeX, using EuroPhys.sty, one eps figure included, accepted for publication in Europhys. Let

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