Interaction between static holes in a quantum dimer model on the kagome lattice

A quantum dimer model (QDM) on the kagome lattice with an extensive ground-state entropy was recently introduced [Phys. Rev. B 67, 214413 (2003)]. The ground-state energy of this QDM in presence of one and two static holes is investigated by means of exact diagonalizations on lattices containing up to 144 kagome sites. The interaction energy between the holes (at distances up to 7 lattice spacings) is evaluated and the results show no indication of confinement at large hole separations.Comment: 6 pages, 3 figures. IOP style files included. To appear in J. Phys.: Condens. Matter, Proceedings of the HFM2003 conference, Grenobl

Random projections and the optimization of an algorithm for phase retrieval

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule. For a general class of algorithms, where the basic iteration is specified by the difference map, solutions are associated with fixed points of the map, the attractive character of which determines the effectiveness of the algorithm. The behavior of the difference map near fixed points is controlled by the relative orientation of the tangent spaces of the two constraint subspaces employed by the map. Since the dimensionalities involved are always large in practical applications, it is appropriate to use random matrix theory ideas to analyze the average-case convergence at fixed points. Optimal values of the gamma parameters of the difference map are found which differ somewhat from the values previously obtained on the assumption of orthogonal tangent spaces.Comment: 15 page

Stability of the hard-sphere icosahedral quasilattice

The stability of the hard-sphere icosahedral quasilattice is analyzed using the differential formulation of the generalized effective liquid approximation. We find that the icosahedral quasilattice is metastable with respect to the hard-sphere crystal structures. Our results agree with recent findings by McCarley and Ashcroft [Phys. Rev. B {\bf 49}, 15600 (1994)] carried out using the modified weighted density approximation.Comment: 15 pages, 2 figures available from authors upon request, (revtex), submitted to Phys. Rev.

The Entropy of Square-Free Words

Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds. Finally, we present an approximate formula which is asymptotically exact with rapid convergence in the number of letters.Comment: 18 page

Quantum Entanglement in Heisenberg Antiferromagnets

Entanglement sharing among pairs of spins in Heisenberg antiferromagnets is investigated using the concurrence measure. For a nondegenerate S=0 ground state, a simple formula relates the concurrence to the diagonal correlation function. The concurrence length is seen to be extremely short. A few finite clusters are studied numerically, to see the trend in higher dimensions. It is argued that nearest-neighbour concurrence is zero for triangular and Kagome lattices. The concurrences in the maximal-spin states are explicitly calculated, where the concurrence averaged over all pairs is larger than the S=0 states.Comment: 7 pages, 3 figure

Magnetic Properties of Undoped C60C_{60}

The Heisenberg antiferromagnet, which arises from the large $U$ Hubbard model, is investigated on the $C_{60}$ molecule and other fullerenes. The connectivity of $C_{60}$ leads to an exotic classical ground state with nontrivial topology. We argue that there is no phase transition in the Hubbard model as a function of $U/t$, and thus the large $U$ solution is relevant for the physical case of intermediate coupling. The system undergoes a first order metamagnetic phase transition. We also consider the S=1/2 case using perturbation theory. Experimental tests are suggested.Comment: 12 pages, 3 figures (included

Recursion and Path-Integral Approaches to the Analytic Study of the Electronic Properties of C60C_{60}

The recursion and path-integral methods are applied to analytically study the electronic structure of a neutral $C_{60}$ molecule. We employ a tight-binding Hamiltonian which considers both the $s$ and $p$ valence electrons of carbon. From the recursion method, we obtain closed-form {\it analytic} expressions for the $\pi$ and $\sigma$ eigenvalues and eigenfunctions, including the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states, and the Green's functions. We also present the local densities of states around several ring clusters, which can be probed experimentally by using, for instance, a scanning tunneling microscope. {}From a path-integral method, identical results for the energy spectrum are also derived. In addition, the local density of states on one carbon atom is obtained; from this we can derive the degree of degeneracy of the energy levels.Comment: 19 pages, RevTex, 6 figures upon reques

A study of long range order in certain two-dimensional frustrated lattices

We have studied the Heisenberg antiferromagnets on two-dimensional frustrated lattices, triangular and kagome lattices using linear spin-wave theory. A collinear ground state ordering is possible if one of the three bonds in each triangular plaquette of the lattice becomes weaker or frustrated. We study spiral order in the Heisenberg model along with Dzyaloshinskii-Moriya (DM) interaction and in the presence of a magnetic field. The quantum corrections to the ground state energy and sublattice magnetization are calculated analytically in the case of triangular lattice with nearesr-neighbour interaction. The corrections depend on the DM interaction strength and the magnetic field. We find that the DM interaction stabilizes the long-range order, reducing the effect of quantum fluctuations. Similar conclusions are reached for the kagome lattice. We work out the linear spin-wave theory at first with only nearest-neighbour (nn) terms for the kagome lattice. We find that the nn interaction is not sufficient to remove the effects of low energy fluctuations. The flat branch in the excitation spectrum becomes dispersive on addition of furthet neighbour interactions. The ground state energy and the excitation spectrum have been obtained for various cases.Comment: 18 pages, 9 figure