Scaling behavior of the energy gap of spin-1/2 AF-Heisenberg chain in both uniform and staggered fields

We have studied the energy gap of the 1D AF-Heisenberg model in the presence of both uniform ($H$) and staggered ($h$) magnetic fields using the exact diagonalization technique. We have found that the opening of the gap in the presence of a staggered field scales with $h^{\nu}$, where $\nu=\nu(H)$ is the critical exponent and depends on the uniform field. With respect to the range of the staggered magnetic field, we have identified two regimes through which the $H$-dependence of the real critical exponent $\nu(H)$ can be numerically calculated. Our numerical results are in good agreement with the results obtained by theoretical approaches

Directed abelian algebras and their applications to stochastic models

To each directed acyclic graph (this includes some D-dimensional lattices) one can associate some abelian algebras that we call directed abelian algebras (DAA). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground state wavefunctions (stationary states probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and choose Hamiltonians linear in the generators, in the finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent $z = D$. One possible application of the DAA is to sandpile models. In the paper we present this application considering one and two dimensional lattices. In the one dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent $\sigma_{\tau} = 3/2$). We study the local densityof particles inside large avalanches showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found $\sigma_{\tau} = 1.782 \pm 0.005$.Comment: 14 pages, 9 figure

From conformal invariance to quasistationary states

In a conformal invariant one-dimensional stochastic model, a certain non-local perturbation takes the system to a new massless phase of a special kind. The ground-state of the system is an adsorptive state. Part of the finite-size scaling spectrum of the evolution Hamiltonian stays unchanged but some levels go exponentially to zero for large lattice sizes becoming degenerate with the ground-state. As a consequence one observes the appearance of quasistationary states which have a relaxation time which grows exponentially with the size of the system. Several initial conditions have singled out a quasistationary state which has in the finite-size scaling limit the same properties as the stationary state of the conformal invariant model.Comment: 20 pages, 15 figure

Preventing Advanced Persistent Threats in Complex Control Networks

An Advanced Persistent Threat (APT) is an emerging attack against Industrial Control and Automation Systems, that is executed over a long period of time and is difficult to detect. In this context, graph theory can be applied to model the interaction among nodes and the complex attacks affecting them, as well as to design recovery techniques that ensure the survivability of the network. Accordingly, we leverage a decision model to study how a set of hierarchically selected nodes can collaborate to detect an APT within the network, concerning the presence of changes in its topology. Moreover, we implement a response service based on redundant links that dynamically uses a secret sharing scheme and applies a flexible routing protocol depending on the severity of the attack. The ultimate goal is twofold: ensuring the reachability between nodes despite the changes and preventing the path followed by messages from being discovered.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

The phase diagram of the anisotropic Spin-1 Heisenberg Chain

We applied the Density Matrix Renormalization Group to the XXZ spin-1 quantum chain. In studing this model we aim to clarify controversials about the point where the massive Haldane phase appears.Comment: 2 pages (standart LaTex), 1 figure (PostScript) uuencode

Bethe Ansatz and boundary energy of the open spin-1/2 XXZ chain

We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider a case where at most two of the boundary parameters {{$\alpha_-$,$\alpha_+$,$\beta_-$,$\beta_+$}} are nonzero. A generalization of the Baxter $T-Q$ equation that involves more than one independent $Q$ is described. We use this solution to compute the boundary energy of the chain in the thermodynamic limit. We conclude the paper with a review of some results for the general integrable boundary terms, where all six boundary parameters are arbitrary.Comment: 6 pages, Latex; contribution to the XVth International Colloquium on Integrable Systems and Quantum Symmetries, Prague, June 2006. To appear in Czechoslovak Journal of Physics (2006); (v2) Typos corrected and a new line added in the Acknowledgments sectio

Numerical evidences of spin-1/2 chain approaching spin-1 chain

In this article, we study the one dimensional Heisenberg spin-1/2 alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and density matrix renormalization groups (DMRG) method, we discuss how the system approaches to the AF uniform spin-1 chain under certain condition. When the ratio of AF to FM coupling strength}$\alpha$ $(\alpha=J_{AF}/J_{F})$ \textit{is very small, the physical quantities of the alternating bond chain such as the spin-spin correlation, the string correlation function and the spin density coincide with that of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with small}$\alpha$\textit{limit. In addition, the Haldane gap of the AF uniform spin-1 chain is 4-times of the gap of the system considered.Comment: 9pages,8page

Magnetic properties of the spin S=1/2S=1/2 Heisenberg chain with hexamer modulation of exchange

We consider the spin-1/2 Heisenberg chain with alternating spin exchange %on even and odd sites in the presence of additional modulation of exchange on odd bonds with period three. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective $XXZ$ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped string order into the only one gapless L\"uttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to 1/3 and 2/3 of the saturation value. These phases reveal themselves also in magnetization curve as plateaus at corresponding values of magnetization. As the result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.Comment: 21 pages, 5 figures, Journal of Physics: Condensed Matter, 24, 116002, (2012

The Yang-Baxter equation for PT invariant nineteen vertex models

We study the solutions of the Yang-Baxter equation associated to nineteen vertex models invariant by the parity-time symmetry from the perspective of algebraic geometry. We determine the form of the algebraic curves constraining the respective Boltzmann weights and found that they possess a universal structure. This allows us to classify the integrable manifolds in four different families reproducing three known models besides uncovering a novel nineteen vertex model in a unified way. The introduction of the spectral parameter on the weights is made via the parameterization of the fundamental algebraic curve which is a conic. The diagonalization of the transfer matrix of the new vertex model and its thermodynamic limit properties are discussed. We point out a connection between the form of the main curve and the nature of the excitations of the corresponding spin-1 chains.Comment: 43 pages, 6 figures and 5 table