Superballistic Diffusion of Entanglement in Disordered Spin Chains

We study the dynamics of a single excitation in an infinite XXZ spin chain, which is launched from the origin. We study the time evolution of the spread of entanglement in the spin chain and obtain an expression for the second order spatial moment of concurrence, about the origin, for both ordered and disordered chains. In this way, we show that a finite central disordered region can lead to sustained superballistic growth in the second order spatial moment of entanglement within the chain.Comment: 5 pages, 1 figur

Renormalization group transformations on quantum states

We construct a general renormalization group transformation on quantum states, independent of any Hamiltonian dynamics of the system. We illustrate this procedure for translational invariant matrix product states in one dimension and show that product, GHZ, W and domain wall states are special cases of an emerging classification of the fixed points of this coarse--graining transformation.Comment: 5 pages, 2 figur

Zero dimensional area law in a gapless fermion system

The entanglement entropy of a gapless fermion subsystem coupled to a gapless bulk by a "weak link" is considered. It is demonstrated numerically that each independent weak link contributes an entropy proportional to lnL, where L is linear dimension of the subsystem.Comment: 6 pages, 11 figures; added 3d computatio

Density of defects and the scaling law of the entanglement entropy in quantum phase transition of one dimensional spin systems induced by a quench

We have studied quantum phase transition induced by a quench in different one dimensional spin systems. Our analysis is based on the dynamical mechanism which envisages nonadiabaticity in the vicinity of the critical point. This causes spin fluctuation which leads to the random fluctuation of the Berry phase factor acquired by a spin state when the ground state of the system evolves in a closed path. The two-point correlation of this phase factor is associated with the probability of the formation of defects. In this framework, we have estimated the density of defects produced in several one dimensional spin chains. At the critical region, the entanglement entropy of a block of $L$ spins with the rest of the system is also estimated which is found to increase logarithmically with $L$. The dependence on the quench time puts a constraint on the block size $L$. It is also pointed out that the Lipkin-Meshkov-Glick model in point-splitting regularized form appears as a combination of the XXX model and Ising model with magnetic field in the negative z-axis. This unveils the underlying conformal symmetry at criticality which is lost in the sharp point limit. Our analysis shows that the density of defects as well as the scaling behavior of the entanglement entropy follows a universal behavior in all these systems.Comment: 4 figures, Accepted in Phys. Rev.

Violation of area-law scaling for the entanglement entropy in spin 1/2 chains

Entanglement entropy obeys area law scaling for typical physical quantum systems. This may naively be argued to follow from locality of interactions. We show that this is not the case by constructing an explicit simple spin chain Hamiltonian with nearest neighbor interactions that presents an entanglement volume scaling law. This non-translational model is contrived to have couplings that force the accumulation of singlet bonds across the half chain. Our result is complementary to the known relation between non-translational invariant, nearest neighbor interacting Hamiltonians and QMA complete problems.Comment: 9 pages, 4 figure

Concepción multinivélica y cuasidescomponible de sistemas complejos. Aplicación a la informática

El interés por el estudio (diseño análisis, descripción) de sistemas complejos se debe a factores muy diversos, que van desde el desarrollo de las ciencias sociales y naturales hasta los logros espectaculares de la tecnología

The Hidden Spatial Geometry of Non-Abelian Gauge Theories

The Gauss law constraint in the Hamiltonian form of the $SU(2)$ gauge theory of gluons is satisfied by any functional of the gauge invariant tensor variable $\phi^{ij} = B^{ia} B^{ja}$. Arguments are given that the tensor $G_{ij} = (\phi^{-1})_{ij}\,\det B$ is a more appropriate variable. When the Hamiltonian is expressed in terms of $\phi$ or $G$, the quantity $\Gamma^i_{jk}$ appears. The gauge field Bianchi and Ricci identities yield a set of partial differential equations for $\Gamma$ in terms of $G$. One can show that $\Gamma$ is a metric-compatible connection for $G$ with torsion, and that the curvature tensor of $\Gamma$ is that of an Einstein space. A curious 3-dimensional spatial geometry thus underlies the gauge-invariant configuration space of the theory, although the Hamiltonian is not invariant under spatial coordinate transformations. Spatial derivative terms in the energy density are singular when $\det G=\det B=0$. These singularities are the analogue of the centrifugal barrier of quantum mechanics, and physical wave-functionals are forced to vanish in a certain manner near $\det B=0$. It is argued that such barriers are an inevitable result of the projection on the gauge-invariant subspace of the Hilbert space, and that the barriers are a conspicuous way in which non-abelian gauge theories differ from scalar field theories.Comment: 19 pages, TeX, CTP #223

Fibromyalgia and therapeutic exercise: Qualitative systematic review

Objetivos: El objetivo de esta revisión es determinar qué ejercicio es más eficaz para reducir la sintomatología de la fibromialgia. Estrategia de búsqueda: Se realizaron búsquedas en las principales bases de datos de las ciencias de la salud: PEDro, PubMed, Cochrane Plus, ISI (Web of Knowledge), y PsycINFO, y en las revistas no indexadas del área, entre marzo y octubre de 2013. Resultados: Se analizó el nivel de evidencia y se aplicaron criterios de exclusión e inclusión para obtener 32 artículos en la revisión, clasificados en 5 categorías en función del tipo de ejercicio. Todos ellos eran ensayos clínicos aleatorios. Conclusiones: El ejercicio terapéutico es eficaz para reducir la sintomatología de la fibromialgia. El ejercicio acuático, el combinado y las actividades alternativas parecen más eficaces para el tratamiento de puntos sensibles, de la depresión, y tiene mayores niveles de adherencia terapéutica. Para el tratamiento del resto de síntomas, todos los tipos de ejercicio tienen similares resultadosObjective: The goal of this review is to determine which exercise is the best to reduce the symptomatology of fibromyalgia. Search Strategy: Intervention studies in fibromyalgia were retrieved through searches in the main health-science databases: PEDro, PubMed, Cochrane Plus, ISI (Web of Knowledge), y PsycINFO, and in in publications of the field, Fisioterapia y Cuestiones de Fisioterapia, between March and October 2013. Results: After applying inclusion and exclusion criteria, and analyze the level of evidence, 32 publications were accepted in this review, classified in 5 different categories, depending on the type of activity. They were all randomized clinical trials. Conclusions: Exercise is effective for reducing symptomatology of fibromyalgia. Aquatic and combined exercise, and alternative activities seem to be more accurate in the treatment of tender points, depression, and they have higher levels of adherence. Relating to the rest of the symptoms, every other type of exercise has similar resul