101 research outputs found
Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems
We study the relation between the recently defined localizable entanglement
and generalized correlations in quantum spin systems. Differently from the
current belief, the localizable entanglement is always given by the average of
a generalized string. Using symmetry arguments we show that in most spin 1/2
and spin 1 systems the localizable entanglement reduces to the spin-spin or
string correlations, respectively. We prove that a general class of spin 1
systems, which includes the Heisenberg model, can be used as perfect quantum
channel. These conclusions are obtained in analytic form and confirm some
results found previously on numerical grounds.Comment: 5 pages, RevTeX
Entanglement and magnetic order
In recent years quantum statistical mechanics have benefited of cultural
interchanges with quantum information science. There is a bulk of evidence that
quantifying the entanglement allows a fine analysis of many relevant properties
of many-body quantum systems. Here we review the relation between entanglement
and the various type of magnetic order occurring in interacting spin systems.Comment: 29 pages, 10 eps figures. Review article for the special issue
"Entanglement entropy in extended systems" in J. Phys. A, edited by P.
Calabrese, J. Cardy and B. Doyo
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
Tensor network states for the description of quantum many-body systems / Tensornetzwerkzustände zur Beschreibung von Quantenvielteilchensystemen
Geometric Entanglement and Quantum Phase Transition in Generalized Cluster-XY models
In this work, we investigate quantum phase transition (QPT) in a generic
family of spin chains using the ground-state energy, the energy gap, and the
geometric measure of entanglement (GE). In many of prior works, GE per site was
used. Here, we also consider GE per block with each block size being two. This
can be regarded as a coarse grain of GE per site. We introduce a useful
parameterization for the family of spin chains that includes the XY models with
n-site interaction, the GHZ-cluster model and a cluster-antiferromagnetic
model, the last of which exhibits QPT between a symmetry-protected topological
(SPT) phase and a symmetry-breaking antiferromagnetic phase. As the models are
exactly solvable, their ground-state wavefunctions can be obtained and thus
their GE can be studied. It turns out that the overlap of the ground states
with translationally invariant product states can be exactly calculated and
hence the GE can be obtained via further parameter optimization. The QPTs
exhibited in these models are detected by the energy gap and singular behavior
of geometric entanglement. In particular, the XzY model exhibits transitions
from the nontrivial SPT phase to a trivial paramagnetic phase. Moreover, the
halfway XY model exhibits a first-order transition across the Barouch-McCoy
circle, on which it was only a crossover in the standard XY model.Comment: 29 pages, 12 figure
The Ongoing Impact of Modular Localization on Particle Theory
Modular localization is the concise conceptual formulation of causal
localization in the setting of local quantum physics. Unlike QM it does not
refer to individual operators but rather to ensembles of observables which
share the same localization region, as a result it explains the probabilistic
aspects of QFT in terms of the impure KMS nature arising from the local
restriction of the pure vacuum. Whereas it played no important role in the
perturbation theory of low spin particles, it becomes indispensible for
interactions which involve higher spin fields, where is leads to the
replacement of the operator (BRST) gauge theory setting in Krein space by a new
formulation in terms of stringlocal fields in Hilbert space. The main purpose
of this paper is to present new results which lead to a rethinking of important
issues of the Standard Model concerning massive gauge theories and the Higgs
mechanism. We place these new findings into the broader context of ongoing
conceptual changes within QFT which already led to new nonperturbative
constructions of models of integrable QFTs. It is also pointed out that modular
localization does not support ideas coming from string theory, as extra
dimensions and Kaluza-Klein dimensional reductions outside quasiclassical
approximations. Apart from hologarphic projections on null-surfaces, holograhic
relations between QFT in different spacetime dimensions violate the causal
completeness property, this includes in particular the Maldacena conjecture.
Last not least, modular localization sheds light onto unsolved problems from
QFT's distant past since it reveals that the Einstein-Jordan conundrum is
really an early harbinger of the Unruh effect.Comment: a small text overlap with unpublished arXiv:1201.632
Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I (The two antagonistic localizations and their asymptotic compatibility)
It is shown that there are significant conceptual differences between QM and
QFT which make it difficult to view the latter as just a relativistic extension
of the principles of QM. At the root of this is a fundamental distiction
between Born-localization in QM (which in the relativistic context changes its
name to Newton-Wigner localization) and modular localization which is the
localization underlying QFT, after one separates it from its standard
presentation in terms of field coordinates. The first comes with a probability
notion and projection operators, whereas the latter describes causal
propagation in QFT and leads to thermal aspects of locally reduced finite
energy states. The Born-Newton-Wigner localization in QFT is only applicable
asymptotically and the covariant correlation between asymptotic in and out
localization projectors is the basis of the existence of an invariant
scattering matrix. In this first part of a two part essay the modular
localization (the intrinsic content of field localization) and its
philosophical consequences take the center stage. Important physical
consequences of vacuum polarization will be the main topic of part II. Both
parts together form a rather comprehensive presentation of known consequences
of the two antagonistic localization concepts, including the those of its
misunderstandings in string theory.Comment: 63 pages corrections, reformulations, references adde
Hidden symmetry breaking in quantum spin systems with applications to measurement-based quantum computation
We extend the hidden symmetry breaking picture, first proposed by Kennedy and Tasaki in the context of the Haldane phase, to a wider class of symmetry-protected topological (SPT) phases. We construct a generalization of the Kennedy-Tasaki transformation that transforms SPT phases into symmetry-breaking phases and relates long-range order in the latter to the more subtle “string order” in the former. In doing so we directly connect the form of the Kennedy-Tasaki transformation to the modern formulation of SPT order. We apply our generalized Kennedy-Tasaki transformation to solve the following problem in quantum information theory. We consider the 2-D cluster state, a simple “toy model” of a locally interacting system whose ground state is a universal resource for MBQC. We prove that, in the presence of a perturbation to the interaction Hamiltonian, the perturbed ground state remains a universal resource. We do this by using the generalized Kennedy-Tasaki transformation to prove that, if we employ the techniques of fault-tolerant quantum computation, the ground states of models in an appropriate SPT phases can serve as universal resources for MBQC provided that the symmetry-breaking is sufficiently strong in the symmetry-breaking phase obtained through the generalized Kennedy-Tasaki transformation
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