4,519 research outputs found
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
Entanglement entropy and conformal field theory
We review the conformal field theory approach to entanglement entropy. We
show how to apply these methods to the calculation of the entanglement entropy
of a single interval, and the generalization to different situations such as
finite size, systems with boundaries, and the case of several disjoint
intervals. We discuss the behaviour away from the critical point and the
spectrum of the reduced density matrix. Quantum quenches, as paradigms of
non-equilibrium situations, are also considered.Comment: 39 Pages, 10 figures. Review article for the special issue
"Entanglement entropy in extended systems" in J. Phys. A. V2 Refs added,
typos correcte
Entanglement Entropy and Quantum Field Theory
We carry out a systematic study of entanglement entropy in relativistic
quantum field theory. This is defined as the von Neumann entropy S_A=-Tr rho_A
log rho_A corresponding to the reduced density matrix rho_A of a subsystem A.
For the case of a 1+1-dimensional critical system, whose continuum limit is a
conformal field theory with central charge c, we re-derive the result
S_A\sim(c/3) log(l) of Holzhey et al. when A is a finite interval of length l
in an infinite system, and extend it to many other cases: finite systems,finite
temperatures, and when A consists of an arbitrary number of disjoint intervals.
For such a system away from its critical point, when the correlation length \xi
is large but finite, we show that S_A\sim{\cal A}(c/6)\log\xi, where \cal A is
the number of boundary points of A. These results are verified for a free
massive field theory, which is also used to confirm a scaling ansatz for the
case of finite-size off-critical systems, and for integrable lattice models,
such as the Ising and XXZ models, which are solvable by corner transfer matrix
methods. Finally the free-field results are extended to higher dimensions, and
used to motivate a scaling form for the singular part of the entanglement
entropy near a quantum phase transition.Comment: 33 pages, 2 figures. Our results for more than one interval are in
general incorrect. A note had been added discussing thi
Corrections to scaling for block entanglement in massive spin-chains
We consider the Renyi entropies S_n in one-dimensional massive integrable
models diagonalizable by means of corner transfer matrices (as Heisenberg and
Ising spin chains). By means of explicit examples and using the relation of
corner transfer matrix with the Virasoro algebra, we show that close to a
conformal invariant critical point, when the correlation length xi is finite
but large, the corrections to the scaling are of the unusual form xi^(-x/n),
with x the dimension of a relevant operator in the conformal theory. This is
reminiscent of the results for gapless chains and should be valid for any
massive one-dimensional model close to a conformal critical point.Comment: 12 pages, no figures. v2 corrected typo
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
Entropy in quantum chromodynamics
We review the role of zero-temperature entropy in several closely-related
contexts in QCD. The first is entropy associated with disordered condensates,
including . The second is vacuum entropy arising from QCD
solitons such as center vortices, yielding confinement and chiral symmetry
breaking. The third is entanglement entropy, which is entropy associated with a
pure state, such as the QCD vacuum, when the state is partially unobserved and
unknown. Typically, entanglement entropy of an unobserved three-volume scales
not with the volume but with the area of its bounding surface. The fourth
manifestation of entropy in QCD is the configurational entropy of
light-particle world-lines and flux tubes; we argue that this entropy is
critical for understanding how confinement produces chiral symmetry breakdown,
as manifested by a dynamically-massive quark, a massless pion, and a condensate.Comment: 22 pages, 2 figures. Preprint version of invited review for Modern
Physics Letters
Priming access to natural-object and trait category hierarchies on pronunciation, lexical decision, and category verification tasks
Lexical decision, pronunciation, and category verification response times (RTs) to natural object and trait hierarchies were measured. Prime and target words consisted of both superordinate and subordinate object and trait category members. Trait words were categorized as desirable and undesirable (Hampson, et al., 1986). Subjects\u27 RTs to object and undesirable trait words displayed similar patterns. In all experiments, RTs to natural-object subordinate target words were significantly more rapid compared to superordinate words. This same pattern was also true for the undesirable traits, but reached significance in only the lexical decision task. The facilitation effect of the prime reached significance for the natural-objects in the category verification experiment and for the undesirable traits in the lexical decision experiment. This pattern of facilitation by the prime were consistent for natural-objects and undesirable traits across all experiments. In each experiment the opposite pattern of results were found for desirable traits. In the pronunciation and lexical decision experiments RTs to desirable superordinate trait words were significantly more rapid compared to desirable subordinate trait words. In all experiments the facilitation by desirable superordinate trait word primes was significantly greater compared to undesirable superordinate trait words. Post-experiment questionnaires indicated that subjects\u27 judgment of the logical hierarchy entailment asymmetries were highly consistent with the norms. Regression analysis of subjects\u27 judgments of the logical entailment between category stimulus pairs indicated no significant systematic relationship. Implications for research on attribution, category memory, and clinical research on cognitive assessment are discussed
Time-dependence of correlation functions following a quantum quench
We show that the time-dependence of correlation functions in an extended
quantum system in d dimensions, which is prepared in the ground state of some
hamiltonian and then evolves without dissipation according to some other
hamiltonian, may be extracted using methods of boundary critical phenomena in
d+1 dimensions. For d=1 particularly powerful results are available using
conformal field theory. These are checked against those available from solvable
models. They may be explained in terms of a picture, valid more generally,
whereby quasiparticles, entangled over regions of the order of the correlation
length in the initial state, then propagate classically through the system.Comment: 4+ pages, Corrected Typo
The Ubiquitous 'c': from the Stefan-Boltzmann Law to Quantum Information
I discuss various aspects of the role of the conformal anomaly number c in 2-
and 1+1-dimensional critical behaviour: its appearance as the analogue of
Stefan's constant, its fundamental role in conformal field theory, in the
classification of 2d universality classes, and as a measure of quantum
entanglement, among other topics.Comment: 8 pages, 2 figures. Boltzmann Medal Lecture, Statphys24, Cairns 2010.
v3: minor revision
- …