Scaling of entanglement between separated blocks in spin chains at criticality

We compute the entanglement between separated blocks in certain spin models showing that at criticality this entanglement is a function of the ratio of the separation to the length of the blocks and can be written as a product of a power law and an exponential decay. It thereby interpolates between the entanglement of individual spins and blocks of spins. It captures features of correlation functions at criticality as well as the monogamous nature of entanglement. We exemplify invariant features of this entanglement to microscopic changes within the same universality class. We find this entanglement to be invariant with respect to simultaneous scale transformations of the separation and the length of the blocks. As a corollary, this study estimates the entanglement between separated regions of those quantum fields to which the considered spin models map at criticality.Comment: 4 pages, 3 figures; comments welcom

AER Neuro-Inspired interface to Anthropomorphic Robotic Hand

Address-Event-Representation (AER) is a communication protocol for transferring asynchronous events between VLSI chips, originally developed for neuro-inspired processing systems (for example, image processing). Such systems may consist of a complicated hierarchical structure with many chips that transmit data among them in real time, while performing some processing (for example, convolutions). The information transmitted is a sequence of spikes coded using high speed digital buses. These multi-layer and multi-chip AER systems perform actually not only image processing, but also audio processing, filtering, learning, locomotion, etc. This paper present an AER interface for controlling an anthropomorphic robotic hand with a neuro-inspired system.Unión Europea IST-2001-34124 (CAVIAR)Ministerio de Ciencia y Tecnología TIC-2003-08164-C03-02Ministerio de Ciencia y Tecnología TIC2000-0406-P4- 0

Fracton-elasticity duality on curved manifolds

Mechanical properties of crystals on curved substrates mix elastic, geometric and topological degrees of freedom. In order to elucidate properties of such crystals we formulate the low-energy effective action that combines metric degrees of freedom with displacement fields and defects. We propose new dualities for elasticity coupled to curved geometry formulated in terms of tensor gauge theories. We show that the metric degrees of freedom, evolving akin to linearized gravity are mapped to tensors with three indices. When coupled to crystals these degrees of freedom become gapped and, in the presence of dislocations and disclinations, multivalued. The elastic degrees of freedom remain gapless and mapped to symmetric gauge fields with two indices. In the dual formulation, topological defects, which act as sources for the gauge fields, are fractons or excitations with restricted mobility. We show that mobility restrictions are manifest only when singularities in both displacement fields and metric are taken into account.Comment: 5 pages, 1 figur

Extraction of Pure Entangled States from Many Body Systems by Distant Local Projections

We study the feasibility of extracting a pure entangled state of non-complementary, and potentially well separated, regions of a quantum many-body system. It is shown that this can indeed be accomplished in non-equilibrium scenarios as well as the ground state of the considered spin chain models when one locally measures observables such as magnetization in separated blocks of spins. A general procedure is presented, which can search for the optimal way to extract a pure entangled state through local projections. Our results indicate a connection of the projective extraction of entanglement to good quantum numbers of the underlying Hamiltonian.Comment: 7 pages, 5 figures. Comments welcom

Emulación del sistema músculo-esqueletal y el control de movimiento en una plataforma experimental

Muchos fisiólogos han observado que el músculo humano o animal es una especie de tejido elástico (como un muelle) con componentes contráctiles, los cuales dan una longitud de umbral modificable neuralmente para el desarrollo de fuerzas. La determinación de las fuerzas del músculo durante el movimiento no es solamente esencial para el análisis de las cargas internas que actúan en los huesos y articulaciones, si no que también contribuyen ha entender más profundamente los controladores neuronales. Los sistemas de control biológicos han sido estudiados como una posible inspiración para la construción de controladores de sistemas robóticos. En este trabajo, se diseño e implemento un sistema biomecánico que tiene propiedades mécanicas casi similares a las de un brazo humano o animal. En este sistema se implementaron modelos matemáticos del músculo biológico, para la generación de fuerzas en el músculo esqueletal total. Además, se desarrollo una red cortical para el control de movimientos voluntarios con restricciones neurofisiológicas y psicofísicas motoras. El controlador neuronal es propuesto para realizar el seguimiento de trajectorias deseadas en la articulación de un simple eslabón controlado por un par de actuadores agonista-antagonista con propiedades musculares. El sistema es capaz de ejecutar movimientos de alcance voluntarios, con perfiles de velocidad en forma de campana bajo perturbaciones. Los resultados experimentales muestran que el sistema presenta las propiedades básicas del músculoesqueletal las cuales son las relaciones fuerza-longitud y fuerza-velocidad. El controlador neuronal permite controlar los movimientos deseados y compesar las fuerzas externas.Se agradece el apoyo recibido por los miembros del grupo de investigación de Neurotecnología, Control y Robótica (NEUROCOR) del departamento de Ingeniería de Sistemas y Automática de la Universidad Politécnica de Cartagena. Este trabajo fue financiado en parte por la CICYTTIC99- 0446-C02-01, y por el proyecto SYNERAGH - BRE2-CT980797 BRITE EURAM- de Investigación Básica

Holographic View on Quantum Correlations and Mutual Information between Disjoint Blocks of a Quantum Critical System

In (d+1) dimensional Multiscale Entanglement Renormalization Ansatz (MERA) networks, tensors are connected so as to reproduce the discrete, (d + 2) holographic geometry of Anti de Sitter space (AdSd+2) with the original system lying at the boundary. We analyze the MERA renormalization flow that arises when computing the quantum correlations between two disjoint blocks of a quantum critical system, to show that the structure of the causal cones characteristic of MERA, requires a transition between two different regimes attainable by changing the ratio between the size and the separation of the two disjoint blocks. We argue that this transition in the MERA causal developments of the blocks may be easily accounted by an AdSd+2 black hole geometry when the mutual information is computed using the Ryu-Takayanagi formula. As an explicit example, we use a BTZ AdS3 black hole to compute the MI and the quantum correlations between two disjoint intervals of a one dimensional boundary critical system. Our results for this low dimensional system not only show the existence of a phase transition emerging when the conformal four point ratio reaches a critical value but also provide an intuitive entropic argument accounting for the source of this instability. We discuss the robustness of this transition when finite temperature and finite size effects are taken into account.Comment: 21 pages, 5 figures. Abstract and Figure 1 has been modified. Minor modifications in Section 1 and Section

Holographic Geometry of Entanglement Renormalization in Quantum Field Theories

We study a conjectured connection between the AdS/CFT and a real-space quantum renormalization group scheme, the multi-scale entanglement renormalization ansatz (MERA). By making a close contact with the holographic formula of the entanglement entropy, we propose a general definition of the metric in the MERA in the extra holographic direction, which is formulated purely in terms of quantum field theoretical data. Using the continuum version of the MERA (cMERA), we calculate this emergent holographic metric explicitly for free scalar boson and free fermions theories, and check that the metric so computed has the properties expected from AdS/CFT. We also discuss the cMERA in a time-dependent background induced by quantum quench and estimate its corresponding metric.Comment: 42pages, 9figures, reference added, minor chang

Boundary States as Holographic Duals of Trivial Spacetimes

We study real-space quantum entanglement included in conformally invariant boundary states in conformal field theories (CFTs). First, we argue that boundary states essentially have no real-space entanglement by computing the entanglement entropy when we bipartite the system into two spatial regions. From the viewpoint of holography, this shows that boundary states are dual to trivial spacetimes of zero spactime volume. Next, we point out that a continuous multiscale entanglement renormalization ansatz (cMERA) for any CFTs can be formulated by employing a boundary state as its infrared unentangled state with an appropriate regularization. Exploiting this idea, we propose an approximation scheme of cMERA construction for general CFTs.Comment: 30 pages, 4 figure

Entanglement Entropy from a Holographic Viewpoint

The entanglement entropy has been historically studied by many authors in order to obtain quantum mechanical interpretations of the gravitational entropy. The discovery of AdS/CFT correspondence leads to the idea of holographic entanglement entropy, which is a clear solution to this important problem in gravity. In this article, we would like to give a quick survey of recent progresses on the holographic entanglement entropy. We focus on its gravitational aspects, so that it is comprehensible to those who are familiar with general relativity and basics of quantum field theory.Comment: Latex, 30 pages, invited review for Classical and Quantum Gravity, minor correction