Bose-Hubbard model on two-dimensional line graphs

We construct a basis for the many-particle ground states of the positive hopping Bose-Hubbard model on line graphs of finite 2-connected planar bipartite graphs at sufficiently low filling factors. The particles in these states are localized on non-intersecting vertex-disjoint cycles of the line graph which correspond to non-intersecting edge-disjoint cycles of the original graph. The construction works up to a critical filling factor at which the cycles are close-packed.Comment: 9 pages, 5 figures, figures and conclusions update

Experimental application of LANDSAT to geobotanical prospecting of serpentine outcrops in the central Appalachian Piedmont of North America

The use of LANDSAT as a tool for geobotanical prospecting was studied in a 13,137 sq km area from southeastern Pennsylvania to northern Virginia. Vegetation differences between known serpentine and non-sepentine sites were most easily distinguished on early summer images. A multispectral signature was derived from vegetation of two known serpentine sites and a map was produced of 159 similar signatures of vegetation in the study area. Authenticity of the serpentine nature of the mapped sites was checked via geochemical analysis of collected soils from 14% of the sites. Overall success of geobotanical prospecting was about 35% for the total study area. When vegetation distribution was taken into account, the success rate was 67% for the region north of the Potomac, demonstrates the effectiveness of the multispectral satellite for quickly and accurately locating mineral sensitive vegetation communities over vast tracts of land

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.

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

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-band excitonic states in Kagome lattice on semiconductor surface

Excitonic properties in the Kagome lattice system, which is produced by quantum wires on semiconductor surfaces, are investigated by using the exact diagonalization of a tight binding model. It is shown that due to the existence of flat bands the binding energy of exciton becomes remarkably large in the two-dimensional Kagome lattice compared to that in one-dimensional lattice, and the exciton Bohr radius is quite small as large as a lattice constant. We also discuss the magnetic field effects on the exciton binding energy and the stability of exciton against the creation of charged exciton and biexciton.Comment: 5 pages, 5 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

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

Magnetic field effects on two-dimensional Kagome lattices

Magnetic field effects on single-particle energy bands (Hofstadter butterfly), Hall conductance, flat-band ferromagnetism, and magnetoresistance of two-dimensional Kagome lattices are studied. The flat-band ferromagnetism is shown to be broken as the flat-band has finite dispersion in the magnetic field. A metal-insulator transition induced by the magnetic field (giant negative magnetoresistance) is predicted. In the half-filled flat band, the ferromagnetic-paramagnetic transition and the metal-insulator one occur simultaneously at a magnetic field for strongly interacting electrons. All of the important magnetic fields effects should be observable in mesoscopic systems such as quantum dot superlattices.Comment: 10 pages, 4 figures, and 1 tabl