496 research outputs found
Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
We present a general scheme for the calculation of the Renyi entropy of a
subsystem in quantum many-body models that can be efficiently simulated via
quantum Monte Carlo. When the simulation is performed at very low temperature,
the above approach delivers the entanglement Renyi entropy of the subsystem,
and it allows to explore the crossover to the thermal Renyi entropy as the
temperature is increased. We implement this scheme explicitly within the
Stochastic Series expansion as well as within path-integral Monte Carlo, and
apply it to quantum spin and quantum rotor models. In the case of quantum
spins, we show that relevant models in two dimensions with reduced symmetry (XX
model or hardcore bosons, transverse-field Ising model at the quantum critical
point) exhibit an area law for the scaling of the entanglement entropy.Comment: 5+1 pages, 4+1 figure
Flow networks: A characterization of geophysical fluid transport
We represent transport between different regions of a fluid domain by flow
networks, constructed from the discrete representation of the Perron-Frobenius
or transfer operator associated to the fluid advection dynamics. The procedure
is useful to analyze fluid dynamics in geophysical contexts, as illustrated by
the construction of a flow network associated to the surface circulation in the
Mediterranean sea. We use network-theory tools to analyze the flow network and
gain insights into transport processes. In particular we quantitatively relate
dispersion and mixing characteristics, classically quantified by Lyapunov
exponents, to the degree of the network nodes. A family of network entropies is
defined from the network adjacency matrix, and related to the statistics of
stretching in the fluid, in particular to the Lyapunov exponent field. Finally
we use a network community detection algorithm, Infomap, to partition the
Mediterranean network into coherent regions, i.e. areas internally well mixed,
but with little fluid interchange between them.Comment: 16 pages, 15 figures. v2: published versio
Entanglement, Purity, and Information Entropies in Continuous Variable Systems
Quantum entanglement of pure states of a bipartite system is defined as the
amount of local or marginal ({\em i.e.}referring to the subsystems) entropy.
For mixed states this identification vanishes, since the global loss of
information about the state makes it impossible to distinguish between quantum
and classical correlations. Here we show how the joint knowledge of the global
and marginal degrees of information of a quantum state, quantified by the
purities or in general by information entropies, provides an accurate
characterization of its entanglement. In particular, for Gaussian states of
continuous variable systems, we classify the entanglement of two--mode states
according to their degree of total and partial mixedness, comparing the
different roles played by the purity and the generalized entropies in
quantifying the mixedness and bounding the entanglement. We prove the existence
of strict upper and lower bounds on the entanglement and the existence of
extremally (maximally and minimally) entangled states at fixed global and
marginal degrees of information. This results allow for a powerful, operative
method to measure mixed-state entanglement without the full tomographic
reconstruction of the state. Finally, we briefly discuss the ongoing extension
of our analysis to the quantification of multipartite entanglement in highly
symmetric Gaussian states of arbitrary -mode partitions.Comment: 16 pages, 5 low-res figures, OSID style. Presented at the
International Conference ``Entanglement, Information and Noise'', Krzyzowa,
Poland, June 14--20, 200
Entanglement-assisted local operations and classical communications conversion in the quantum critical systems
Conversions between the ground states in quantum critical systems via
entanglement-assisted local operations and classical communications (eLOCC) are
studied. We propose a new method to reveal the different convertibility by
local operations when a quantum phase transition occurs. We have studied the
ground state local convertibility in the one dimensional transverse field Ising
model, XY model and XXZ model. It is found that the eLOCC convertibility sudden
changes at the phase transition points. In transverse field Ising model the
eLOCC convertibility between the first excited state and the ground state are
also distinct for different phases. The relation between the order of quantum
phase transitions and the local convertibility is discussed.Comment: 7 pages, 5 figures, 5 table
A transform of complementary aspects with applications to entropic uncertainty relations
Even though mutually unbiased bases and entropic uncertainty relations play
an important role in quantum cryptographic protocols they remain ill
understood. Here, we construct special sets of up to 2n+1 mutually unbiased
bases (MUBs) in dimension d=2^n which have particularly beautiful symmetry
properties derived from the Clifford algebra. More precisely, we show that
there exists a unitary transformation that cyclically permutes such bases. This
unitary can be understood as a generalization of the Fourier transform, which
exchanges two MUBs, to multiple complementary aspects. We proceed to prove a
lower bound for min-entropic entropic uncertainty relations for any set of
MUBs, and show that symmetry plays a central role in obtaining tight bounds.
For example, we obtain for the first time a tight bound for four MUBs in
dimension d=4, which is attained by an eigenstate of our complementarity
transform. Finally, we discuss the relation to other symmetries obtained by
transformations in discrete phase space, and note that the extrema of discrete
Wigner functions are directly related to min-entropic uncertainty relations for
MUBs.Comment: 16 pages, 2 figures, v2: published version, clarified ref [30
Exact Matrix Product States for Quantum Hall Wave Functions
We show that the model wave functions used to describe the fractional quantum
Hall effect have exact representations as matrix product states (MPS). These
MPS can be implemented numerically in the orbital basis of both finite and
infinite cylinders, which provides an efficient way of calculating arbitrary
observables. We extend this approach to the charged excitations and numerically
compute their Berry phases. Finally, we present an algorithm for numerically
computing the real-space entanglement spectrum starting from an arbitrary
orbital basis MPS, which allows us to study the scaling properties of the
real-space entanglement spectra on infinite cylinders. The real-space
entanglement spectrum obeys a scaling form dictated by the edge conformal field
theory, allowing us to accurately extract the two entanglement velocities of
the Moore-Read state. In contrast, the orbital space spectrum is observed to
scale according to a complex set of power laws that rule out a similar
collapse.Comment: 10 pages and Appendix, v3 published versio
Morphology of Fine-Particle Monolayers Deposited on Nanopatterned Substrates
We study the effect of the presence of a regular substrate pattern on the
irreversible adsorption of nanosized and colloid particles. Deposition of disks
of radius is considered, with the allowed regions for their center
attachment at the planar surface consisting of square cells arranged in a
square lattice pattern. We study the jammed state properties of a generalized
version of the random sequential adsorption model for different values of the
cell size, , and cell-cell separation, . The model shows a surprisingly
rich behavior in the space of the two dimensionless parameters
and . Extensive Monte Carlo simulations for system sizes of
square lattice unit cells were performed by utilizing an
efficient algorithm, to characterize the jammed state morphology.Comment: 11 pages, 10 figures, 3 table
Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics
A consistent generalization of statistical mechanics is obtained by applying
the maximum entropy principle to a trace-form entropy and by requiring that
physically motivated mathematical properties are preserved. The emerging
differential-functional equation yields a two-parameter class of generalized
logarithms, from which entropies and power-law distributions follow: these
distributions could be relevant in many anomalous systems. Within the specified
range of parameters, these entropies possess positivity, continuity, symmetry,
expansibility, decisivity, maximality, concavity, and are Lesche stable. The
Boltzmann-Shannon entropy and some one parameter generalized entropies already
known belong to this class. These entropies and their distribution functions
are compared, and the corresponding deformed algebras are discussed.Comment: Version to appear in PRE: about 20% shorter, references updated, 13
PRE pages, 3 figure
A second row Parking Paradox
We consider two variations of the discrete car parking problem where at every
vertex of the integers a car arrives with rate one, now allowing for parking in
two lines. a) The car parks in the first line whenever the vertex and all of
its nearest neighbors are not occupied yet. It can reach the first line if it
is not obstructed by cars already parked in the second line (screening). b) The
car parks according to the same rules, but parking in the first line can not be
obstructed by parked cars in the second line (no screening). In both models, a
car that can not park in the first line will attempt to park in the second
line. If it is obstructed in the second line as well, the attempt is discarded.
We show that both models are solvable in terms of finite-dimensional ODEs. We
compare numerically the limits of first and second line densities, with time
going to infinity. While it is not surprising that model a) exhibits an
increase of the density in the second line from the first line, more remarkably
this is also true for model b), albeit in a less pronounced way.Comment: 11 pages, 4 figure
Unique additive information measures - Boltzmann-Gibbs-Shannon, Fisher and beyond
It is proved that the only additive and isotropic information measure that
can depend on the probability distribution and also on its first derivative is
a linear combination of the Boltzmann-Gibbs-Shannon and Fisher information
measures. Power law equilibrium distributions are found as a result of the
interaction of the two terms. The case of second order derivative dependence is
investigated and a corresponding additive information measure is given.Comment: 10 pages, 1 figures, shortene
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