11,469 research outputs found
Entanglement entropy of two disjoint intervals in conformal field theory
We study the entanglement of two disjoint intervals in the conformal field
theory of the Luttinger liquid (free compactified boson). Tr\rho_A^n for any
integer n is calculated as the four-point function of a particular type of
twist fields and the final result is expressed in a compact form in terms of
the Riemann-Siegel theta functions. In the decompactification limit we provide
the analytic continuation valid for all model parameters and from this we
extract the entanglement entropy. These predictions are checked against
existing numerical data.Comment: 34 pages, 7 figures. V2: Results for small x behavior added, typos
corrected and refs adde
Corrections to scaling in entanglement entropy from boundary perturbations
We investigate the corrections to scaling of the Renyi entropies of a region
of size l at the end of a semi-infinite one-dimensional system described by a
conformal field theory when the corrections come from irrelevant boundary
operators. The corrections from irrelevant bulk operators with scaling
dimension x have been studied by Cardy and Calabrese (2010), and they found not
only the expected corrections of the form l^(4-2x) but also unusual corrections
that could not have been anticipated by finite-size scaling arguments alone.
However, for the case of perturbations from irrelevant boundary operators we
find that the only corrections that can occur to leading order are of the form
l^(2-2x_b) for boundary operators with scaling dimension x_b < 3/2, and l^(-1)
when x_b > 3/2. When x_b=3/2 they are of the form l^(-1)log(l). A marginally
irrelevant boundary perturbation will give leading corrections going as
log(l)^(-3). No unusual corrections occur when perturbing with a boundary
operator.Comment: 8 pages. Minor improvements and updated references. Published versio
Field-theory results for three-dimensional transitions with complex symmetries
We discuss several examples of three-dimensional critical phenomena that can
be described by Landau-Ginzburg-Wilson theories. We present an
overview of field-theoretical results obtained from the analysis of high-order
perturbative series in the frameworks of the and of the
fixed-dimension d=3 expansions. In particular, we discuss the stability of the
O(N)-symmetric fixed point in a generic N-component theory, the critical
behaviors of randomly dilute Ising-like systems and frustrated spin systems
with noncollinear order, the multicritical behavior arising from the
competition of two distinct types of ordering with symmetry O() and
O() respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200
Geometrical optics analysis of the short-time stability properties of the Einstein evolution equations
Many alternative formulations of Einstein's evolution have lately been
examined, in an effort to discover one which yields slow growth of
constraint-violating errors. In this paper, rather than directly search for
well-behaved formulations, we instead develop analytic tools to discover which
formulations are particularly ill-behaved. Specifically, we examine the growth
of approximate (geometric-optics) solutions, studied only in the future domain
of dependence of the initial data slice (e.g. we study transients). By
evaluating the amplification of transients a given formulation will produce, we
may therefore eliminate from consideration the most pathological formulations
(e.g. those with numerically-unacceptable amplification). This technique has
the potential to provide surprisingly tight constraints on the set of
formulations one can safely apply. To illustrate the application of these
techniques to practical examples, we apply our technique to the 2-parameter
family of evolution equations proposed by Kidder, Scheel, and Teukolsky,
focusing in particular on flat space (in Rindler coordinates) and Schwarzchild
(in Painleve-Gullstrand coordinates).Comment: Submitted to Phys. Rev.
Entanglement Entropy of Two Spheres
We study the entanglement entropy S_{AB} of a massless free scalar field on
two spheres A and B whose radii are R_1 and R_2, respectively, and the distance
between the centers of them is r. The state of the massless free scalar field
is the vacuum state. We obtain the result that the mutual information
S_{A;B}:=S_A+S_B-S_{AB} is independent of the ultraviolet cutoff and
proportional to the product of the areas of the two spheres when r>>R_1,R_2,
where S_A and S_B are the entanglement entropy on the inside region of A and B,
respectively. We discuss possible connections of this result with the physics
of black holes.Comment: 17 pages, 9 figures; v4, added references, revised argument in
section V, a typo in eq.(25) corrected, published versio
Entanglement versus mutual information in quantum spin chains
The quantum entanglement of a bipartite quantum Ising chain is compared
with the mutual information between the two parts after a local measurement
of the classical spin configuration. As the model is conformally invariant, the
entanglement measured in its ground state at the critical point is known to
obey a certain scaling form. Surprisingly, the mutual information of classical
spin configurations is found to obey the same scaling form, although with a
different prefactor. Moreover, we find that mutual information and the
entanglement obey the inequality in the ground state as well as in a
dynamically evolving situation. This inequality holds for general bipartite
systems in a pure state and can be proven using similar techniques as for
Holevo's bound.Comment: 10 pages, 3 figure
Quantum Quench from a Thermal Initial State
We consider a quantum quench in a system of free bosons, starting from a
thermal initial state. As in the case where the system is initially in the
ground state, any finite subsystem eventually reaches a stationary thermal
state with a momentum-dependent effective temperature. We find that this can,
in some cases, even be lower than the initial temperature. We also study
lattice effects and discuss more general types of quenches.Comment: 6 pages, 2 figures; short published version, added references, minor
change
Entanglement properties of quantum spin chains
We investigate the entanglement properties of a finite size 1+1 dimensional
Ising spin chain, and show how these properties scale and can be utilized to
reconstruct the ground state wave function. Even at the critical point, few
terms in a Schmidt decomposition contribute to the exact ground state, and to
physical properties such as the entropy. Nevertheless the entanglement here is
prominent due to the lower-lying states in the Schmidt decomposition.Comment: 5 pages, 6 figure
Quantum phase transitions in the Kondo-necklace model: Perturbative continuous unitary transformation approach
The Kondo-necklace model can describe magnetic low-energy limit of strongly
correlated heavy fermion materials. There exist multiple energy scales in this
model corresponding to each phase of the system. Here, we study quantum phase
transition between the Kondo-singlet phase and the antiferromagnetic long-range
ordered phase, and show the effect of anisotropies in terms of quantum
information properties and vanishing energy gap. We employ the "perturbative
continuous unitary transformations" approach to calculate the energy gap and
spin-spin correlations for the model in the thermodynamic limit of one, two,
and three spatial dimensions as well as for spin ladders. In particular, we
show that the method, although being perturbative, can predict the expected
quantum critical point, where the gap of low-energy spectrum vanishes, which is
in good agreement with results of other numerical and Green's function
analyses. In addition, we employ concurrence, a bipartite entanglement measure,
to study the criticality of the model. Absence of singularities in the
derivative of concurrence in two and three dimensions in the Kondo-necklace
model shows that this model features multipartite entanglement. We also discuss
crossover from the one-dimensional to the two-dimensional model via the ladder
structure.Comment: 12 pages, 6 figure
Entanglement entropy of a quantum unbinding transition and entropy of DNA
Two significant consequences of quantum fluctuations are entanglement and
criticality. Entangled states may not be critical but a critical state shows
signatures of universality in entanglement. A surprising result found here is
that the entanglement entropy may become arbitrarily large and negative near
the dissociation of a bound pair of quantum particles. Although apparently
counter-intuitive, it is shown to be consistent and essential for the phase
transition, by mapping to a classical problem of DNA melting. We associate the
entanglement entropy to a subextensive part of the entropy of DNA bubbles,
which is responsible for melting. The absence of any extensivity requirement in
time makes this negative entropy an inevitable consequence of quantum mechanics
in continuum. Our results encompass quantum critical points and first-order
transitions in general dimensions.Comment: v2: 6 pages, 3 figures (title modified, more details and figures
added
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