810 research outputs found
R\'enyi entropy of a line in two-dimensional Ising models
We consider the two-dimensional (2d) Ising model on a infinitely long
cylinder and study the probabilities to observe a given spin
configuration along a circular section of the cylinder. These probabilities
also occur as eigenvalues of reduced density matrices in some Rokhsar-Kivelson
wave-functions. We analyze the subleading constant to the R\'enyi entropy
and discuss its scaling properties at the
critical point. Studying three different microscopic realizations, we provide
numerical evidence that it is universal and behaves in a step-like fashion as a
function of , with a discontinuity at the Shannon point . As a
consequence, a field theoretical argument based on the replica trick would fail
to give the correct value at this point. We nevertheless compute it numerically
with high precision. Two other values of the R\'enyi parameter are of special
interest: and are related in a simple way to the
Affleck-Ludwig boundary entropies associated to free and fixed boundary
conditions respectively.Comment: 8 pages, 6 figures, 2 tables. To be submitted to Physical Review
Phase transition in the R\'enyi-Shannon entropy of Luttinger liquids
The R\'enyi-Shannon entropy associated to critical quantum spins chain with
central charge is shown to have a phase transition at some value of
the R\'enyi parameter which depends on the Luttinger parameter (or
compactification radius R). Using a new replica-free formulation, the entropy
is expressed as a combination of single-sheet partition functions evaluated at
dependent values of the stiffness. The transition occurs when a vertex
operator becomes relevant at the boundary. Our numerical results (exact
diagonalizations for the XXZ and models) are in agreement with the
analytical predictions: above the subleading and universal
contribution to the entropy is for open chains, and
for periodic ones (R=1 at the free fermion point). The replica
approach used in previous works fails to predict this transition and turns out
to be correct only for . From the point of view of two-dimensional
Rokhsar-Kivelson states, the transition reveals a rich structure in the
entanglement spectra.Comment: 4 pages, 3 figure
R\'enyi entanglement entropies in quantum dimer models : from criticality to topological order
Thanks to Pfaffian techniques, we study the R\'enyi entanglement entropies
and the entanglement spectrum of large subsystems for two-dimensional
Rokhsar-Kivelson wave functions constructed from a dimer model on the
triangular lattice. By including a fugacity on some suitable bonds, one
interpolates between the triangular lattice (t=1) and the square lattice (t=0).
The wave function is known to be a massive topological liquid for
whereas it is a gapless critical state at t=0. We mainly consider two
geometries for the subsystem: that of a semi-infinite cylinder, and the
disk-like setup proposed by Kitaev and Preskill [Phys. Rev. Lett. 96, 110404
(2006)]. In the cylinder case, the entropies contain an extensive term --
proportional to the length of the boundary -- and a universal sub-leading
constant . Fitting these cylinder data (up to a perimeter of L=32
sites) provides with a very high numerical accuracy ( at t=1 and
at ). In the topological liquid phase we find
, independent of the fugacity and the R\'enyi parameter
. At t=0 we recover a previously known result,
for . In the disk-like geometry --
designed to get rid of the boundary contributions -- we find an entropy in the whole massive phase whatever , in agreement with
the result of Flammia {\it et al.} [Phys. Rev. Lett. 103, 261601 (2009)]. Some
results for the gapless limit are discussed.Comment: 33 pages, 17 figures, minor correction
Preserving Partial Solutions while Relaxing Constraint Networks
International audienceThis paper is about transforming constraint net- works to accommodate additional constraints in specific ways. The focus is on two intertwined issues. First, we investigate how partial solutions to an initial network can be preserved from the potential impact of additional constraints. Second, we study how more permissive constraints, which are intended to enlarge the set of solutions, can be accommodated in a constraint network. These two problems are studied in the general case and the light is shed on their relationship. A case study is then investigated where a more permissive additional constraint is taken into account through a form of network relaxation, while some previous partial solutions are preserved at the same time
A CSP solver focusing on FAC variables
International audienceThe contribution of this paper is twofold. On the one hand, it introduces a concept of FAC variables in discrete Constraint Satisfaction Prob- lems (CSPs). FAC variables can be discovered by local search techniques and powerfully exploited by MAC-based methods. On the other hand, a novel syn- ergetic combination schema between local search paradigms, generalized arc- consistency and MAC-based algorithms is presented. By orchestrating a multiple- way flow of information between these various fully integrated search compo- nents, it often proves more competitive than the usual techniques on most classes of instances
Relax!
International audienceThis paper is concerned with a form of relaxation of constraint networks. The focus is on situations where additional constraints are intended to extend a non- empty set of preexisting solutions. These constraints require a speci c treatment since merely inserting them inside the network would lead to their preemption by more restrictive ones. Several approaches to handle these additional constraints are investigated from con- ceptual and experimental points of view
Physically Based Rigid Registration of 3-D Free-Form Objects : application to Medical Imaging
The registration of 3-D objects is an important problem in computer vision and especially in medical imaging. It arises when data acquired by different sensors and/or at different times have to be fused. Under the basic assumption that the objects to be registered are rigid, the problem is to recover the six parameters of a rigid transformation. If landmarks or common characteristics % between both objects to register are not available, the problem has to be solved by an iterative method. However such methods are inevitably attracted to local minima. This paper presents a novel iterative method designed for the rigid registration of 3-D objects. Its originality lies in its physical basis: instead of minimizing an energy function with respect to the parameters of the rigid transformation (the classical approach) the minimization is achieved by studying the motion of a rigid object in a potential field. In particular, we consider the kinetic energy of the solid during the registration process, which allows it to «jump over» some local maxima of the potential energy and so avoid some local minima of that energy. We present extensive experimental results on real 3-D medical images. In this particular application, we perform the matching process with the whole segmented volumes
Shannon and entanglement entropies of one- and two-dimensional critical wave functions
We study the Shannon entropy of the probability distribution resulting from
the ground-state wave function of a one-dimensional quantum model. This entropy
is related to the entanglement entropy of a Rokhsar-Kivelson-type wave function
built from the corresponding two-dimensional classical model. In both critical
and massive cases, we observe that it is composed of an extensive part
proportional to the length of the system and a subleading universal constant
S_0. In c=1 critical systems (Tomonaga-Luttinger liquids), we find that S_0 is
a simple function of the boson compactification radius. This finding is based
on a field-theoretical analysis of the Dyson-Gaudin gas related to dimer and
Calogero-Sutherland models. We also performed numerical demonstrations in the
dimer models and the spin-1/2 XXZ chain. In a massive (crystal) phase, S_0 is
related to the ground-state degeneracy. We also examine this entropy in the
Ising chain in a transverse field as an example showing a c=1/2 critical point.Comment: 23 pages, 19 figures, to be published in Physical Review
Results of two years of a mooring over a Posidonia Oceanica seagrass meadow (Corsica, France)
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