59 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
Spin Chains in an External Magnetic Field. Closure of the Haldane Gap and Effective Field Theories
We investigate both numerically and analytically the behaviour of a spin-1
antiferromagnetic (AFM) isotropic Heisenberg chain in an external magnetic
field. Extensive DMRG studies of chains up to N=80 sites extend previous
analyses and exhibit the well known phenomenon of the closure of the Haldane
gap at a lower critical field H_c1. We obtain an estimate of the gap below
H_c1. Above the lower critical field, when the correlation functions exhibit
algebraic decay, we obtain the critical exponent as a function of the net
magnetization as well as the magnetization curve up to the saturation (upper
critical) field H_c2. We argue that, despite the fact that the SO(3) symmetry
of the model is explicitly broken by the field, the Haldane phase of the model
is still well described by an SO(3) nonlinear sigma-model. A mean-field theory
is developed for the latter and its predictions are compared with those of the
numerical analysis and with the existing literature.Comment: 11 pages, 4 eps figure
Long-distance entanglement and quantum teleportation in XX spin chains
Isotropic XX models of one-dimensional spin-1/2 chains are investigated with
the aim to elucidate the formal structure and the physical properties that
allow these systems to act as channels for long-distance, high-fidelity quantum
teleportation. We introduce two types of models: I) open, dimerized XX chains,
and II) open XX chains with small end bonds. For both models we obtain the
exact expressions for the end-to-end correlations and the scaling of the energy
gap with the length of the chain. We determine the end-to-end concurrence and
show that model I) supports true long-distance entanglement at zero
temperature, while model II) supports {\it ``quasi long-distance''}
entanglement that slowly falls off with the size of the chain. Due to the
different scalings of the gaps, respectively exponential for model I) and
algebraic in model II), we demonstrate that the latter allows for efficient
qubit teleportation with high fidelity in sufficiently long chains even at
moderately low temperatures.Comment: 9 pages, 6 figure
Qubit Teleportation and Transfer across Antiferromagnetic Spin Chains
We explore the capability of spin-1/2 chains to act as quantum channels for
both teleportation and transfer of qubits. Exploiting the emergence of
long-distance entanglement in low-dimensional systems [Phys. Rev. Lett. 96,
247206 (2006)], here we show how to obtain high communication fidelities
between distant parties. An investigation of protocols of teleportation and
state transfer is presented, in the realistic situation where temperature is
included. Basing our setup on antiferromagnetic rotationally invariant systems,
both protocols are represented by pure depolarizing channels. We propose a
scheme where channel fidelity close to one can be achieved on very long chains
at moderately small temperature.Comment: 5 pages, 4 .eps figure
Optimal quasi-free approximation:reconstructing the spectrum from ground state energies
The sequence of ground state energy density at finite size, e_{L}, provides
much more information than usually believed. Having at disposal e_{L} for short
lattice sizes, we show how to re-construct an approximate quasi-particle
dispersion for any interacting model. The accuracy of this method relies on the
best possible quasi-free approximation to the model, consistent with the
observed values of the energy e_{L}. We also provide a simple criterion to
assess whether such a quasi-free approximation is valid. As a side effect, our
method is able to assess whether the nature of the quasi-particles is fermionic
or bosonic together with the effective boundary conditions of the model. When
applied to the spin-1/2 Heisenberg model, the method produces a band of Fermi
quasi-particles very close to the exact one of des Cloizeaux and Pearson. The
method is further tested on a spin-1/2 Heisenberg model with explicit
dimerization and on a spin-1 chain with single ion anisotropy. A connection
with the Riemann Hypothesis is also pointed out.Comment: 9 pages, 5 figures. One figure added showing convergence spee
Long-distance entanglement in spin systems
Most quantum system with short-ranged interactions show a fast decay of
entanglement with the distance. In this Letter, we focus on the peculiarity of
some systems to distribute entanglement between distant parties. Even in
realistic models, like the spin-1 Heisenberg chain, sizable entanglement is
present between arbitrarily distant particles. We show that long distance
entanglement appears for values of the microscopic parameters which do not
coincide with known quantum critical points, hence signaling a transition
detected only by genuine quantum correlations.Comment: RevTex, 5 pages, 7 .eps figures Two references added in published
versio
Probability density of quantum expectation values
We consider the quantum expectation value \mathcal{A}=\ of an
observable A over the state |\psi\> . We derive the exact probability
distribution of \mathcal{A} seen as a random variable when |\psi\> varies over
the set of all pure states equipped with the Haar-induced measure. The
probability density is obtained with elementary means by computing its
characteristic function, both for non-degenerate and degenerate observables. To
illustrate our results we compare the exact predictions for few concrete
examples with the concentration bounds obtained using Levy's lemma. Finally we
comment on the relevance of the central limit theorem and draw some results on
an alternative statistical mechanics based on the uniform measure on the energy
shell.Comment: Substantial revision. References adde
Rapidly-converging methods for the location of quantum critical points from finite-size data
We analyze in detail, beyond the usual scaling hypothesis, the finite-size
convergence of static quantities toward the thermodynamic limit. In this way we
are able to obtain sequences of pseudo-critical points which display a faster
convergence rate as compared to currently used methods. The approaches are
valid in any spatial dimension and for any value of the dynamic exponent. We
demonstrate the effectiveness of our methods both analytically on the basis of
the one dimensional XY model, and numerically considering c = 1 transitions
occurring in non integrable spin models. In particular, we show that these
general methods are able to locate precisely the onset of the
Berezinskii-Kosterlitz-Thouless transition making only use of ground-state
properties on relatively small systems.Comment: 9 pages, 2 EPS figures, RevTeX style. Updated to published versio
Finding critical points using improved scaling Ansaetze
Analyzing in detail the first corrections to the scaling hypothesis, we
develop accelerated methods for the determination of critical points from
finite size data. The output of these procedures are sequences of
pseudo-critical points which rapidly converge towards the true critical points.
In fact more rapidly than previously existing methods like the Phenomenological
Renormalization Group approach. Our methods are valid in any spatial
dimensionality and both for quantum or classical statistical systems. Having at
disposal fast converging sequences, allows to draw conclusions on the basis of
shorter system sizes, and can be extremely important in particularly hard cases
like two-dimensional quantum systems with frustrations or when the sign problem
occurs. We test the effectiveness of our methods both analytically on the basis
of the one-dimensional XY model, and numerically at phase transitions occurring
in non integrable spin models. In particular, we show how a new Homogeneity
Condition Method is able to locate the onset of the
Berezinskii-Kosterlitz-Thouless transition making only use of ground-state
quantities on relatively small systems.Comment: 16 pages, 4 figures. New version including more general Ansaetze
basically applicable to all case
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