9 research outputs found
Entanglement evolution after connecting finite to infinite quantum chains
We study zero-temperature XX chains and transverse Ising chains and join an
initially separate finite piece on one or on both sides to an infinite
remainder. In both critical and non-critical systems we find a typical increase
of the entanglement entropy after the quench, followed by a slow decay towards
the value of the homogeneous chain. In the critical case, the predictions of
conformal field theory are verified for the first phase of the evolution, while
at late times a step structure can be observed.Comment: 15 pages, 11 figure
Exact relationship between the entanglement entropies of XY and quantum Ising chains
We consider two prototypical quantum models, the spin-1/2 XY chain and the
quantum Ising chain and study their entanglement entropy, S(l,L), of blocks of
l spins in homogeneous or inhomogeneous systems of length L. By using two
different approaches, free-fermion techniques and perturbational expansion, an
exact relationship between the entropies is revealed. Using this relation we
translate known results between the two models and obtain, among others, the
additive constant of the entropy of the critical homogeneous quantum Ising
chain and the effective central charge of the random XY chain.Comment: 6 page
Entanglement entropy of aperiodic quantum spin chains
We study the entanglement entropy of blocks of contiguous spins in
non-periodic (quasi-periodic or more generally aperiodic) critical Heisenberg,
XX and quantum Ising spin chains, e.g. in Fibonacci chains. For marginal and
relevant aperiodic modulations, the entanglement entropy is found to be a
logarithmic function of the block size with log-periodic oscillations. The
effective central charge, c_eff, defined through the constant in front of the
logarithm may depend on the ratio of couplings and can even exceed the
corresponding value in the homogeneous system. In the strong modulation limit,
the ground state is constructed by a renormalization group method and the
limiting value of c_eff is exactly calculated. Keeping the ratio of the block
size and the system size constant, the entanglement entropy exhibits a scaling
property, however, the corresponding scaling function may be nonanalytic.Comment: 6 pages, 2 figure
Phase diagram of a Bose-Fermi mixture in a one-dimensional optical lattice in terms of fidelity and entanglement
We study the ground-state phase diagram of a Bose-Fermi mixture loaded in a
one-dimensional optical lattice by computing the ground-state fidelity and
quantum entanglement. We find that the fidelity is able to signal quantum phase
transitions between the Luttinger liquid phase, the density-wave phase, and the
phase separation state of the system; and the concurrence can be used to signal
the transition between the density-wave phase and the Ising phase.Comment: 4 pages 3 figure
Entanglement entropy in aperiodic singlet phases
We study the average entanglement entropy of blocks of contiguous spins in
aperiodic XXZ chains which possess an aperiodic singlet phase at least in a
certain limit of the coupling ratios. In this phase, where the ground state
constructed by a real space renormalization group method, consists
(asymptotically) of independent singlet pairs, the average entanglement entropy
is found to be a piecewise linear function of the block size. The enveloping
curve of this function is growing logarithmically with the block size, with an
effective central charge in front of the logarithm which is characteristic for
the underlying aperiodic sequence. The aperiodic sequence producing the largest
effective central charge is identified, and the latter is found to exceed the
central charge of the corresponding homogeneous model. For marginal aperiodic
modulations, numerical investigations performed for the XX model show a
logarithmic dependence, as well, with an effective central charge varying
continuously with the coupling ratio.Comment: 18 pages, 9 figure
Entanglement and correlation functions following a local quench: a conformal field theory approach
We show that the dynamics resulting from preparing a one-dimensional quantum
system in the ground state of two decoupled parts, then joined together and
left to evolve unitarily with a translational invariant Hamiltonian (a local
quench), can be described by means of quantum field theory. In the case when
the corresponding theory is conformal, we study the evolution of the
entanglement entropy for different bi-partitions of the line. We also consider
the behavior of one- and two-point correlation functions. All our findings may
be explained in terms of a picture, that we believe to be valid more generally,
whereby quasiparticles emitted from the joining point at the initial time
propagate semiclassically through the system.Comment: 19 pages, 4 figures, v2 typos corrected and refs adde
Entanglement in Many-Body Systems
The recent interest in aspects common to quantum information and condensed
matter has prompted a prosperous activity at the border of these disciplines
that were far distant until few years ago. Numerous interesting questions have
been addressed so far. Here we review an important part of this field, the
properties of the entanglement in many-body systems. We discuss the zero and
finite temperature properties of entanglement in interacting spin, fermionic
and bosonic model systems. Both bipartite and multipartite entanglement will be
considered. At equilibrium we emphasize on how entanglement is connected to the
phase diagram of the underlying model. The behavior of entanglement can be
related, via certain witnesses, to thermodynamic quantities thus offering
interesting possibilities for an experimental test. Out of equilibrium we
discuss how to generate and manipulate entangled states by means of many-body
Hamiltonians.Comment: 61 pages, 29 figure
Holographic Entanglement Entropy: An Overview
In this article, we review recent progresses on the holographic
understandings of the entanglement entropy in the AdS/CFT correspondence. After
reviewing the general idea of holographic entanglement entropy, we will explain
its applications to confinement/deconfinement phase transitions, black hole
entropy and covariant formulation of holography.Comment: 52 pages, Invited review article for a special issue "Entanglement
entropy in extended quantum systems" in Journal of Physics A, edited by
P.Calabrese, J. Cardy and B. Doyon; (v2) references adde
Entanglement in many-body systems
Recent interest in aspects common to quantum information and condensed matter has prompted a
flurry of activity at the border of these disciplines that were far distant until a few years ago. Numerous
interesting questions have been addressed so far. Here an important part of this field, the properties
of the entanglement in many-body systems, are reviewed. The zero and finite temperature properties
of entanglement in interacting spin, fermion, and boson model systems are discussed. Both bipartite
and multipartite entanglement will be considered. In equilibrium entanglement is shown tightly
connected to the characteristics of the phase diagram. The behavior of entanglement can be related,
via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an
experimental test. Out of equilibrium entangled states are generated and manipulated by means of
many-body Hamiltonians