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

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

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

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