272 research outputs found
Entanglement in a second order quantum phase transition
We consider a system of mutually interacting spin 1/2 embedded in a
transverse magnetic field which undergo a second order quantum phase
transition. We analyze the entanglement properties and the spin squeezing of
the ground state and show that, contrarily to the one-dimensional case, a
cusp-like singularity appears at the critical point , in the
thermodynamic limit. We also show that there exists a value above which the ground state is not spin squeezed despite a
nonvanishing concurrence.Comment: 4 pages, 4 EPS figures, minor corrections added and title change
Geometry of entangled states, Bloch spheres and Hopf fibrations
We discuss a generalization to 2 qubits of the standard Bloch sphere
representation for a single qubit, in the framework of Hopf fibrations of high
dimensional spheres by lower dimensional spheres. The single qubit Hilbert
space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented
S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres
represent the qubit overall phase degree of freedom. For the two qubits case,
the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf
fibration, with S3 fibres and a S4 base. A main striking result is that
suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation
with the standard Schmidt decomposition is also discussedComment: submitted to J. Phys.
Aperiodic Quantum Random Walks
We generalize the quantum random walk protocol for a particle in a
one-dimensional chain, by using several types of biased quantum coins, arranged
in aperiodic sequences, in a manner that leads to a rich variety of possible
wave function evolutions. Quasiperiodic sequences, following the Fibonacci
prescription, are of particular interest, leading to a sub-ballistic
wavefunction spreading. In contrast, random sequences leads to diffusive
spreading, similar to the classical random walk behaviour. We also describe how
to experimentally implement these aperiodic sequences.Comment: 4 pages and 4 figure
Density of states of tight-binding models in the hyperbolic plane
We study the energy spectrum of tight-binding Hamiltonian for regular
hyperbolic tilings. More specifically, we compute the density of states using
the continued-fraction expansion of the Green function on finite-size systems
with more than sites and open boundary conditions. The coefficients of
this expansion are found to quickly converge so that the thermodynamical limit
can be inferred quite accurately. This density of states is in stark contrast
with the prediction stemming from the recently proposed hyperbolic band theory.
Thus, we conclude that the fraction of the energy spectrum described by the
hyperbolic Bloch-like wave eigenfunctions vanishes in the thermodynamical
limit.Comment: 12 pages, 7 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
Landau level broadening, hyperuniformity, and discrete scale invariance
We study the energy spectrum of a two-dimensional electron in the presence of
both a perpendicular magnetic field and a potential. In the limit where the
potential is small compared to the Landau level spacing, we show that the
broadening of Landau levels is simply expressed in terms of the structure
factor of the potential. For potentials that are either periodic or random, we
recover known results. Interestingly, for potentials with a dense Fourier
spectrum made of Bragg peaks (as found, e.g., in quasicrystals), we find an
algebraic broadening with the magnetic field characterized by the
hyperuniformity exponent of the potential. Furthermore, if the potential is
self-similar such that its structure factor has a discrete scale invariance,
the broadening displays log-periodic oscillations together with an algebraic
envelope.Comment: 13 pages, 3 figures, published versio
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
Quasicrystalline three-dimensional foams
We present a numerical study of quasiperiodic foams, in which the bubbles are
generated as duals of quasiperiodic Frank-Kasper phases. These foams are
investigated as potential candidates to the celebrated Kelvin problem for the
partition of three-dimensional space with equal volume bubbles and minimal
surface area. Interestingly, one of the computed structures falls close (but
still slightly above) the best known Weaire-Phelan periodic candidate. This
gives additional clues to understanding the main geometrical ingredients
driving the Kelvin problem
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