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

Yang--Mills Configurations from 3D Riemann--Cartan Geometry

Recently, the {\it spacelike} part of the $SU(2)$ Yang--Mills equations has been identified with geometrical objects of a three--dimensional space of constant Riemann--Cartan curvature. We give a concise derivation of this Ashtekar type (``inverse Kaluza--Klein") {\it mapping} by employing a $(3+1)$--decomposition of {\it Clifford algebra}--valued torsion and curvature two--forms. In the subcase of a mapping to purely axial 3D torsion, the corresponding Lagrangian consists of the translational and Lorentz {\it Chern--Simons term} plus cosmological term and is therefore of purely topological origin.Comment: 14 pages, preprint Cologne-thp-1994-h1

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.

Turkish /h/ deletion : evidence for the interplay of speech perception and phonology

It has been hypothesized that sounds which are less perceptible are more likely to be altered than more salient sounds, the rationale being that the loss of information resulting from a change in a sound which is difficult to perceive is not as great as the loss resulting from a change in a more salient sound. Kohler (1990) suggested that the tendency to reduce articulatory movements is countered by perceptual and social constraints, finding that fricatives are relatively resistant to reduction in colloquial German. Kohler hypothesized that this is due to the perceptual salience of fricatives, a hypothesis which was supported by the results of a perception experiment by Hura, Lindblom, and Diehl (1992). These studies showed that the relative salience of speech sounds is relevant to explaining phonological behavior. An additional factor is the impact of different acoustic environments on the perceptibility of speech sounds. Steriade (1997) found that voicing contrasts are more common in positions where more cues to voicing are available. The P-map, proposed by Steriade (2001a, b), allows the representation of varying salience of segments in different contexts. Many researchers have posited a relationship between speech perception and phonology. The purpose of this paper is to provide experimental evidence for this relationship, drawing on the case of Turkish /h/ deletion

Properties of Hubbard models with degenerate localized single particle eigenstates

We consider the repulsive Hubbard model on a class of lattices or graphs for which there is a large degeneracy of the single particle ground states and where the projector onto the space of single particle ground states is highly reducible. This means that one can find a basis in the space of the single particle ground states such that the support of each single particle ground state belongs to some small cluster and these clusters do not overlap. We show how such lattices can be constructed in arbitrary dimensions. We construct all multi-particle ground states of these models for electron numbers not larger than the number of localized single particle eigenstates. We derive some of the ground state properties, esp. the residual entropy, i.e. the finite entropy density at zero temperature.Comment: 11 pages, no figures. Complete revision of the paper with many change

Flow equations for band--matrices

Continuous unitary transformations can be used to diagonalize or approximately diagonalize a given Hamiltonian. In the last four years, this method has been applied to a variety of models of condensed matter physics and field theory. With a new generator for the continuous unitary transformation proposed in this paper one can avoid some of the problems of former applications. General properties of the new generator are derived. It turns out that the new generator is especially useful for Hamiltonians with a banded structure. Two examples, the Lipkin model, and the spin--boson model are discussed in detail.Comment: 12 pages, one eps-figure, uses epsfig.sty. Accepted for publication in European Physical Journa

Ferromagnetism in the Hubbard model: A constructive approach

It is believed that strong ferromagnetic orders in some solids are generated by subtle interplay between quantum many-body effects and spin-independent Coulomb interactions between electrons. Here we describe our rigorous and constructive approach to ferromagnetism in the Hubbard model, which is a standard idealized model for strongly interacting electrons in a solid. We introduce a class of Hubbard models in any dimensions which are nonsingular in the sense that both the Coulomb interaction and the density of states (at the Fermi level) are finite. We then prove that the ground states of the models exhibit saturated ferromagnetism, i.e., have maximum total spins. Combined with our earlier results, the present work provides nonsingular models of itinerant electrons with only spin-independent interactions where low energy behaviors are proved to be that of a ``healthy'' ferromagnetic insulator.Comment: 34 pages (References have been added in v2. Many small changes have been made in v3. Minor typos fixed in v4.