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

Two-flavour Schwinger model with dynamical fermions in the L\"uscher formalism

We report preliminary results for 2D massive QED with two flavours of Wilson fermions, using the Hermitean variant of L\"uscher's bosonization technique. The chiral condensate and meson masses are obtained. The simplicity of the model allows for high statistics simulations close to the chiral and continuum limit, both in the quenched approximation and with dynamical fermions.Comment: Talk presented at LATTICE96(algorithms), 3 pages, 3 Postscript figures, uses twoside, fleqn, espcrc2, epsf, revised version (details of approx. polynomial

Ordering monomial factors of polynomials in the product representation

The numerical construction of polynomials in the product representation (as used for instance in variants of the multiboson technique) can become problematic if rounding errors induce an imprecise or even unstable evaluation of the polynomial. We give criteria to quantify the effects of these rounding errors on the computation of polynomials approximating the function $1/s$. We consider polynomials both in a real variable $s$ and in a Hermitian matrix. By investigating several ordering schemes for the monomials of these polynomials, we finally demonstrate that there exist orderings of the monomials that keep rounding errors at a tolerable level.Comment: Latex2e file, 7 figures, 32 page

The "Square Kagome" Quantum Antiferromagnet and the Eight Vertex Model

We introduce a two dimensional network of corner-sharing triangles with square lattice symmetry. Properties of magnetic systems here should be similar to those on the kagome lattice. Focusing on the spin half Heisenberg quantum antiferromagnet, we generalise the spin symmetry group from SU(2) to SU(N). In the large N limit, we map the model exactly to the eight vertex model, solved by Baxter. We predict an exponential number of low-lying singlet states, a triplet gap, and a two-peak specific heat. In addition, the large N limit suggests a finite temperature phase transition into a phase with ordered ``resonance loops'' and broken translational symmetry.Comment: 5 pages, revtex, 5 eps figures include

Green's function approach to the magnetic properties of the kagome antiferromagnet

The $S=1/2$ Heisenberg antiferromagnet is studied on the kagom\'e lattice by using a Green's function method based on an appropriate decoupling of the equations of motion. Thermodynamic properties as well as spin-spin correlation functions are obtained and characterize this system as a two-dimensional quantum spin liquid. Spin-spin correlation functions decay exponentially with distance down to low temperature and the calculated missing entropy at T=0 is found to be $0.46\ln{2}$. Within the present scheme, the specific heat exhibits a single peak structure and a $T^2$ dependence at low temperature.Comment: 6 (two-column revtex4) pages, 5 ps figures. Submitted to Phys. Rev.

Spin-1/2 Heisenberg-Antiferromagnet on the Kagome Lattice: High Temperature Expansion and Exact Diagonalisation Studies

For the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the Kagom\'e lattice we calculate the high temperature series for the specific heat and the structure factor. A comparison of the series with exact diagonalisation studies shows that the specific heat has further structure at lower temperature in addition to a high temperature peak at $T\approx 2/3$. At $T=0.25$ the structure factor agrees quite well with results for the ground state of a finite cluster with 36 sites. At this temperature the structure factor is less than two times its $T=\infty$ value and depends only weakly on the wavevector $\bf q$, indicating the absence of magnetic order and a correlation length of less than one lattice spacing. The uniform susceptibility has a maximum at $T\approx 1/6$ and vanishes exponentially for lower temperatures.Comment: 15 pages + 5 figures, revtex, 26.04.9

Quantum spin models with exact dimer ground states

Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground state configuration of all the members of the family on a periodic chain. The ground state is two-fold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh hamiltonian with two-fold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.Comment: 10 pages, 8 figures, revtex, to appear in Phys. Rev.

Quantum dynamics in high codimension tilings: from quasiperiodicity to disorder

We analyze the spreading of wavepackets in two-dimensional quasiperiodic and random tilings as a function of their codimension, i.e. of their topological complexity. In the quasiperiodic case, we show that the diffusion exponent that characterizes the propagation decreases when the codimension increases and goes to 1/2 in the high codimension limit. By constrast, the exponent for the random tilings is independent of their codimension and also equals 1/2. This shows that, in high codimension, the quasiperiodicity is irrelevant and that the topological disorder leads in every case, to a diffusive regime, at least in the time scale investigated here.Comment: 4 pages, 5 EPS figure

How to escape Aharonov-Bohm cages ?

We study the effect of disorder and interactions on a recently proposed magnetic field induced localization mechanism. We show that both partially destroy the extreme confinement of the excitations occuring in the pure case and give rise to unusual behavior. We also point out the role of the edge states that allows for a propagation of the electrons in these systems.Comment: 22 pages, 20 EPS figure

Magneto-thermodynamics of the spin-1/2 Kagome antiferromagnet

In this paper, we use a new hybrid method to compute the thermodynamic behavior of the spin-1/2 Kagome antiferromagnet under the influence of a large external magnetic field. We find a T^2 low-temperature behavior and a very low sensitivity of the specific heat to a strong external magnetic field. We display clear evidence that this low temperature magneto-thermal effect is associated to the existence of low-lying fluctuating singlets, but also that the whole picture (T^2 behavior of Cv and thermally activated spin susceptibility) implies contribution of both non magnetic and magnetic excitations. Comparison with experiments is made.Comment: 4 pages, LaTeX 2.09 and RevTeX with 3 figures embedded in the text. Version to appear in Phys. Rev. Let