316 research outputs found
Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions
Three-dimensional integer partitions provide a convenient representation of
codimension-one three-dimensional random rhombus tilings. Calculating the
entropy for such a model is a notoriously difficult problem. We apply
transition matrix Monte Carlo simulations to evaluate their entropy with high
precision. We consider both free- and fixed-boundary tilings. Our results
suggest that the ratio of free- and fixed-boundary entropies is
, and can be interpreted as the ratio of the
volumes of two simple, nested, polyhedra. This finding supports a conjecture by
Linde, Moore and Nordahl concerning the ``arctic octahedron phenomenon'' in
three-dimensional random tilings
Two-dimensional random tilings of large codimension: new progress
Two-dimensional random tilings of rhombi can be seen as projections of
two-dimensional membranes embedded in hypercubic lattices of higher dimensional
spaces. Here, we consider tilings projected from a -dimensional space. We
study the limiting case, when the quantity , and therefore the number of
different species of tiles, become large. We had previously demonstrated [ICQ6]
that, in this limit, the thermodynamic properties of the tiling become
independent of the boundary conditions. The exact value of the limiting entropy
and finite corrections remain open questions. Here, we develop a mean-field
theory, which uses an iterative description of the tilings based on an analogy
with avoiding oriented walks on a random tiling. We compare the quantities
so-obtained with numerical calculations. We also discuss the role of spatial
correlations.Comment: Proceedings of the 7th International Conference on Quasicrystals
(ICQ7, Stuttgart), 4 pages, 4 figure
Adiabatic Computation - A Toy Model
We discuss a toy model for adiabatic quantum computation which displays some
phenomenological properties expected in more realistic implementations. This
model has two free parameters: the adiabatic evolution parameter and the
parameter which emulates many-variables constrains in the classical
computational problem. The proposed model presents, in the plane, a
line of first order quantum phase transition that ends at a second order point.
The relation between computation complexity and the occurrence of quantum phase
transitions is discussed. We analyze the behavior of the ground and first
excited states near the quantum phase transition, the gap and the entanglement
content of the ground state.Comment: 7 pages, 8 figure
Phase diagram of an extended quantum dimer model on the hexagonal lattice
We introduce a quantum dimer model on the hexagonal lattice that, in addition
to the standard three-dimer kinetic and potential terms, includes a competing
potential part counting dimer-free hexagons. The zero-temperature phase diagram
is studied by means of quantum Monte Carlo simulations, supplemented by
variational arguments. It reveals some new crystalline phases and a cascade of
transitions with rapidly changing flux (tilt in the height language). We
analyze perturbatively the vicinity of the Rokhsar-Kivelson point, showing that
this model has the microscopic ingredients needed for the "devil's staircase"
scenario [E. Fradkin et al., Phys. Rev. B 69, 224415 (2004)], and is therefore
expected to produce fractal variations of the ground-state flux.Comment: Published version. 5 pages + 8 (Supplemental Material), 31
references, 10 color 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
Geometrical approach to SU(2) navigation with Fibonacci anyons
Topological quantum computation with Fibonacci anyons relies on the
possibility of efficiently generating unitary transformations upon
pseudoparticles braiding. The crucial fact that such set of braids has a dense
image in the unitary operations space is well known; in addition, the
Solovay-Kitaev algorithm allows to approach a given unitary operation to any
desired accuracy. In this paper, the latter task is fulfilled with an
alternative method, in the SU(2) case, based on a generalization of the
geodesic dome construction to higher dimension.Comment: 12 pages, 5 figure
Entanglement in a first order quantum phase transition
The phase diagram of spins 1/2 embedded in a magnetic field mutually
interacting antiferromagnetically is determined. Contrary to the ferromagnetic
case where a second order quantum phase transition occurs, a first order
transition is obtained at zero field. The spectrum is computed for a large
number of spins and allows one to study the ground state entanglement
properties which displays a jump of its concurrence at the critical point.Comment: 4 pages, 3 EPS figure
Topological phase for entangled two-qubit states and the representation of the SO(3)group
We discuss the representation of the group by two-qubit maximally
entangled states (MES). We analyze the correspondence between and the
set of two-qubit MES which are experimentally realizable. As a result, we offer
a new interpretation of some recently proposed experiments based on MES.
Employing the tools of quantum optics we treat in terms of two-qubit MES some
classical experiments in neutron interferometry, which showed the -phase
accrued by a spin- particle precessing in a magnetic field. By so doing,
we can analyze the extent to which the recently proposed experiments - and
future ones of the same sort - would involve essentially new physical aspects
as compared with those performed in the past. We argue that the proposed
experiments do extend the possibilities for displaying the double connectedness
of , although for that to be the case it results necessary to map
elements of onto physical operations acting on two-level systems.Comment: 25 pages, 9 figure
A remark on the trace-map for the Silver mean sequence
In this work we study the Silver mean sequence based on substitution rules by
means of a transfer-matrix approach. Using transfer-matrix method we find a
recurrence relation for the traces of general transfer-matrices which
characterizes electronic properties of the quasicrystal in question. We also
find an invariant of the trace-map.Comment: 5 pages, minor improvements in style and presentation of calculation
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