169 research outputs found
Penrose Quantum Antiferromagnet
The Penrose tiling is a perfectly ordered two dimensional structure with
fivefold symmetry and scale invariance under site decimation. Quantum spin
models on such a system can be expected to differ significantly from more
conventional structures as a result of its special symmetries. In one
dimension, for example, aperiodicity can result in distinctive quantum
entanglement properties. In this work, we study ground state properties of the
spin-1/2 Heisenberg antiferromagnet on the Penrose tiling, a model that could
also be pertinent for certain three dimensional antiferromagnetic
quasicrystals. We show, using spin wave theory and quantum Monte Carlo
simulation, that the local staggered magnetizations strongly depend on the
local coordination number z and are minimized on some sites of five-fold
symmetry. We present a simple explanation for this behavior in terms of
Heisenberg stars. Finally we show how best to represent this complex
inhomogeneous ground state, using the "perpendicular space" representation of
the tiling.Comment: 4 pages, 5 figure
Energy level statistics of electrons in a 2D quasicrystal
A numerical study is made of the spectra of a tight-binding hamiltonian on
square approximants of the quasiperiodic octagonal tiling. Tilings may be pure
or random, with different degrees of phason disorder considered. The level
statistics for the randomized tilings follow the predictions of random matrix
theory, while for the perfect tilings a new type of level statistics is found.
In this case, the first-, second- level spacing distributions are well
described by lognormal laws with power law tails for large spacing. In
addition, level spacing properties being related to properties of the density
of states, the latter quantity is studied and the multifractal character of the
spectral measure is exhibited.Comment: 9 pages including references and figure captions, 6 figures available
upon request, LATEX, report-number els
Metal-insulator transition in the Hartree-Fock phase diagram of the fully polarized homogeneous electron gas in two dimensions
We determine numerically the ground state of the two-dimensional, fully
polarized electron gas within the Hartree-Fock approximation without imposing
any particular symmetries on the solutions. At low electronic densities, the
Wigner crystal solution is stable, but for higher densities ( less than
) we obtain a ground state of different symmetry: the charge density
forms a triangular lattice with about 11% more sites than electrons. We prove
analytically that this conducting state with broken translational symmetry has
lower energy than the uniform Fermi gas state in the high density region giving
rise to a metal to insulator transition.Comment: 13 pages, 5 figures, rewrite of 0804.1025 and 0807.077
Icosahedral multi-component model sets
A quasiperiodic packing Q of interpenetrating copies of C, most of them only
partially occupied, can be defined in terms of the strip projection method for
any icosahedral cluster C. We show that in the case when the coordinates of the
vectors of C belong to the quadratic field Q[\sqrt{5}] the dimension of the
superspace can be reduced, namely, Q can be re-defined as a multi-component
model set by using a 6-dimensional superspace.Comment: 7 pages, LaTeX2e in IOP styl
Self-similarity under inflation and level statistics: a study in two dimensions
Energy level spacing statistics are discussed for a two dimensional
quasiperiodic tiling. The property of self-similarity under inflation is used
to write a recursion relation for the level spacing distributions defined on
square approximants to the perfect quasiperiodic structure.
New distribution functions are defined and determined by a combination of
numerical and analytical calculations.Comment: Latex, 13 pages including 6 EPS figures, paper submitted to PR
Classification of one-dimensional quasilattices into mutual local-derivability classes
One-dimensional quasilattices are classified into mutual local-derivability
(MLD) classes on the basis of geometrical and number-theoretical
considerations. Most quasilattices are ternary, and there exist an infinite
number of MLD classes. Every MLD class has a finite number of quasilattices
with inflation symmetries. We can choose one of them as the representative of
the MLD class, and other members are given as decorations of the
representative. Several MLD classes of particular importance are listed. The
symmetry-preserving decorations rules are investigated extensively.Comment: 42 pages, latex, 5 eps figures, Published in JPS
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
Water-seeking behavior in worm-infected crickets and reversibility of parasitic manipulation
One of the most fascinating examples of parasite-induced host manipulation is that of hairworms, first, because they induce a spectacular "suicide” water-seeking behavior in their terrestrial insect hosts and, second, because the emergence of the parasite is not lethal per se for the host that can live several months following parasite release. The mechanisms hairworms use to increase the encounter rate between their host and water remain, however, poorly understood. Considering the selective landscape in which nematomorph manipulation has evolved as well as previously obtained proteomics data, we predicted that crickets harboring mature hairworms would display a modified behavioral response to light. Since following parasite emergence in water, the cricket host and parasitic worm do not interact physiologically anymore, we also predicted that the host would recover from the modified behaviors. We examined the effect of hairworm infection on different behavioral responses of the host when stimulated by light to record responses from uninfected, infected, and ex-infected crickets. We showed that hairworm infection fundamentally modifies cricket behavior by inducing directed responses to light, a condition from which they mostly recover once the parasite is released. This study supports the idea that host manipulation by parasites is subtle, complex, and multidimensiona
Spin waves and local magnetizations on the Penrose tiling
We consider a Heisenberg antiferromagnet on the Penrose tiling, a
quasiperiodic system having an inhomogeneous Neel-ordered ground state. Spin
wave energies and wavefunctions are studied in the linear spin wave
approximation. A linear dispersion law is found at low energies, as in other
bipartite antiferromagnets, with an effective spin wave velocity lower than in
the square lattice. Spatial properties of eigenmodes are characterized in
several different ways. At low energies, eigenstates are relatively extended,
and show multifractal scaling. At higher energies, states are more localized,
and, depending on the energy, confined to sites of a specified coordination
number. The ground state energy of this antiferromagnet, and local staggered
magnetizations are calculated. Perpendicular space projections are presented in
order to show the underlying simplicity of this "complex" ground state. A
simple analytical model, the two-tier Heisenberg star, is presented to explain
the staggered magnetization distribution in this antiferromagnetic system.Comment: 14 pages, 21 figure
Generalized quasiperiodic Rauzy tilings
We present a geometrical description of new canonical -dimensional
codimension one quasiperiodic tilings based on generalized Fibonacci sequences.
These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual
Penrose and icosahedral tilings. Thanks to a natural indexing of the sites
according to their local environment, we easily write down, for any
approximant, the sites coordinates, the connectivity matrix and we compute the
structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change
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