32,228 research outputs found
Entanglement entropy and D1-D5 geometries
http://dx.doi.org/10.1103/PhysRevD.90.066004Giusto, Stefano, and Rodolfo Russo. "Entanglement Entropy and D1-D5 geometries." Physical Review D 90.6 (2014): 066004
Entanglement entropy and quantum field theory: a non-technical introduction
In these proceedings we give a pedagogical and non-technical introduction to
the Quantum Field Theory approach to entanglement entropy. Particular attention
is devoted to the one space dimensional case, with a linear dispersion
relation, that, at a quantum critical point, can be effectively described by a
two-dimensional Conformal Field Theory.Comment: 10 Pages, 2 figures. Talk given at the conference "Entanglement in
Physical and information sciences", Centro Ennio de Giorgi, Pisa, December
200
A class of quantum many-body states that can be efficiently simulated
We introduce the multi-scale entanglement renormalization ansatz (MERA), an
efficient representation of certain quantum many-body states on a D-dimensional
lattice. Equivalent to a quantum circuit with logarithmic depth and distinctive
causal structure, the MERA allows for an exact evaluation of local expectation
values. It is also the structure underlying entanglement renormalization, a
coarse-graining scheme for quantum systems on a lattice that is focused on
preserving entanglement.Comment: 4 pages, 5 figure
Ageing Properties of Critical Systems
In the past few years systems with slow dynamics have attracted considerable
theoretical and experimental interest. Ageing phenomena are observed during
this ever-lasting non-equilibrium evolution. A simple instance of such a
behaviour is provided by the dynamics that takes place when a system is
quenched from its high-temperature phase to the critical point. The aim of this
review is to summarize the various numerical and analytical results that have
been recently obtained for this case. Particular emphasis is put to the
field-theoretical methods that can be used to provide analytical predictions
for the relevant dynamical quantities. Fluctuation-dissipation relations are
discussed and in particular the concept of fluctuation-dissipation ratio (FDR)
is reviewed, emphasizing its connection with the definition of a possible
effective temperature. The Renormalization-Group approach to critical dynamics
is summarized and the scaling forms of the time-dependent non-equilibrium
correlation and response functions of a generic observable are discussed. From
them the universality of the associated FDR follows as an amplitude ratio. It
is then possible to provide predictions for ageing quantities in a variety of
different models. In particular the results for Model A, B, and C dynamics of
the O(N) Ginzburg-Landau Hamiltonian, and Model A dynamics of the weakly dilute
Ising magnet and of a \phi^3 theory, are reviewed and compared with the
available numerical results and exact solutions. The effect of a planar surface
on the ageing behaviour of Model A dynamics is also addressed within the
mean-field approximation.Comment: rvised enlarged version, 72 Pages, Topical Review accepted for
publication on JP
Unusual Corrections to Scaling in Entanglement Entropy
We present a general theory of the corrections to the asymptotic behaviour of
the Renyi entropies which measure the entanglement of an interval A of length L
with the rest of an infinite one-dimensional system, in the case when this is
described by a conformal field theory of central charge c. These can be due to
bulk irrelevant operators of scaling dimension x>2, in which case the leading
corrections are of the expected form L^{-2(x-2)} for values of n close to 1.
However for n>x/(x-2) corrections of the form L^{2-x-x/n} and L^{-2x/n} arise
and dominate the conventional terms. We also point out that the last type of
corrections can also occur with x less than 2. They arise from relevant
operators induced by the conical space-time singularities necessary to describe
the reduced density matrix. These agree with recent analytic and numerical
results for quantum spin chains. We also compute the effect of marginally
irrelevant bulk operators, which give a correction (log L)^{-2}, with a
universal amplitude. We present analogous results for the case when the
interval lies at the end of a semi-infinite system.Comment: 15 pages, no figure
Improving Classifier Performance Assessment of Credit Scoring Models
In evaluating credit scoring predictive power it is common to use the Re-ceiver Operating Characteristics (ROC) curve, the Area Under the Curve(AUC) and the minimum probability-weighted loss. The main weakness of the rst two assessments is not to take the costs of misclassication errors into account and the last one depends on the number of defaults in the credit portfolio. The main purposes of this paper are to provide a curve, called curve of Misclassication Error Loss (MEL), and a classier performance measure that overcome the above-mentioned drawbacks. We prove that the ROC dominance is equivalent to the MEL dominance. Furthermore, we derive the probability distribution of the proposed predictive power measure and we analyse its performance by Monte Carlo simulations. Finally, we apply the suggested methodologies to empirical data on Italian Small and Medium Enterprisers.Performance Assessment, Credit Scoring Modules, Monte Carlo simulations, Italian Enterprisers
The critical behavior of 2-d frustrated spin models with noncollinear order
We study the critical behavior of frustrated spin models with noncollinear
order in two dimensions, including antiferromagnets on a triangular lattice and
fully frustrated antiferromagnets. For this purpose we consider the
corresponding Landau-Ginzburg-Wilson (LGW) Hamiltonian and
compute the field-theoretic expansion to four loops and determine its
large-order behavior. We show the existence of a stable fixed point for the
physically relevant cases of two- and three-component spin models. We also give
a prediction for the critical exponent which is and
for N=3 and 2 respectively.Comment: 11 pages, 8 figure
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