43,886 research outputs found
Entanglement entropy in long-range harmonic oscillators
We study the Von Neumann and R\'enyi entanglement entropy of long-range
harmonic oscillators (LRHO) by both theoretical and numerical means. We show
that the entanglement entropy in massless harmonic oscillators increases
logarithmically with the sub-system size as .
Although the entanglement entropy of LRHO's shares some similarities with the
entanglement entropy at conformal critical points we show that the R\'enyi
entanglement entropy presents some deviations from the expected conformal
behavior. In the massive case we demonstrate that the behavior of the
entanglement entropy with respect to the correlation length is also logarithmic
as the short range case.Comment: Published version, 5 figure
Generalized entanglement entropy
We discuss two measures of entanglement in quantum field theory and their
holographic realizations. For field theories admitting a global symmetry, we
introduce a global symmetry entanglement entropy, associated with the
partitioning of the symmetry group. This quantity is proposed to be related to
the generalized holographic entanglement entropy defined via the partitioning
of the internal space of the bulk geometry. The second measure of quantum field
theory entanglement is the field space entanglement entropy, obtained by
integrating out a subset of the quantum fields. We argue that field space
entanglement entropy cannot be precisely realised geometrically in a
holographic dual. However, for holographic geometries with interior decoupling
regions, the differential entropy provides a close analogue to the field space
entanglement entropy. We derive generic descriptions of such inner throat
regions in terms of gravity coupled to massive scalars and show how the
differential entropy in the throat captures features of the field space
entanglement entropy.Comment: 40 pages, 3 figure
Holographic Entanglement Entropy in P-wave Superconductor Phase Transition
We investigate the behavior of entanglement entropy across the holographic
p-wave superconductor phase transition in an Einstein-Yang-Mills theory with a
negative cosmological constant. The holographic entanglement entropy is
calculated for a strip geometry at AdS boundary. It is found that the
entanglement entropy undergoes a dramatic change as we tune the ratio of the
gravitational constant to the Yang-Mills coupling, and that the entanglement
entropy does behave as the thermal entropy of the background black holes. That
is, the entanglement entropy will show the feature of the second order or first
order phase transition when the ratio is changed. It indicates that the
entanglement entropy is a good probe to investigate the properties of the
holographic phase transition.Comment: 19 pages,15 figures, extended discussion in Sec.5, references adde
On the T-dual renormalisation of entanglement entropy
Imposing T-duality in the renormalisation process of entanglement entropy
leads to new relations between entanglement entropy counter-terms. T-duality is
made explicit by means of the generalised metric of double field theory in the
context of bulk-boundary duality. Double field theory in the bulk naturally
provides the new relations between higher order quantum corrections to
entanglement entropy as well as a systematic approach to understanding
entanglement entropy renormalisation counter-terms. An analogue for
Slavnov-Taylor identities for T-dual counter-terms of entanglement entropy is
envisaged
Renormalization of Entanglement Entropy and the Gravitational Effective Action
The entanglement entropy associated with a spatial boundary in quantum field
theory is UV divergent, with the leading term proportional to the area of the
boundary. For a class of quantum states defined by a path integral, the
Callan-Wilczek formula gives a geometrical definition of the entanglement
entropy. We show that, for this class of quantum states, the entanglement
entropy is rendered UV-finite by precisely the counterterms required to cancel
the UV divergences in the gravitational effective action. In particular, the
leading contribution to the entanglement entropy is given by the renormalized
Bekenstein-Hawking formula, in accordance with a proposal of Susskind and
Uglum. We show that the subleading UV-divergent terms in the entanglement
entropy depend nontrivially on the quantum state. We compute new subleading
terms in the entanglement entropy and find agreement with the Wald entropy
formula for black hole spacetimes with bifurcate Killing horizons. We speculate
that the entanglement entropy of an arbitrary spatial boundary may be a
well-defined observable in quantum gravity.Comment: 26 pages, 2 figures. v2: minor corrections and clarification
Monogamous property of generalized W states in three-qubit systems in terms of relative entropy of entanglement
Because of the difficulty in getting the analytic formula of relative entropy
of entanglement, it becomes troublesome to study the monogamy relations of
relative entropy of entanglement for three-qubit pure states. However, we find
that all generalized W states have the monogamous property for relative entropy
of entanglement by calculating the relative entropy of entanglement for the
reduced states of the generalized W states in three-qubit systems.Comment: 9 pages, 1 figur
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