Construction of spin models displaying quantum criticality from quantum field theory

We provide a method for constructing finite temperature states of one-dimensional spin chains displaying quantum criticality. These models are constructed using correlators of products of quantum fields and have an analytical purification. Their properties can be investigated by Monte-Carlo simulations, which enable us to study the low-temperature phase diagram and to show that it displays a region of quantum criticality. The mixed states obtained are shown to be close to the thermal state of a simple nearest neighbour Hamiltonian.Comment: 10 pages, 6 figure

Qubism: self-similar visualization of many-body wavefunctions

A visualization scheme for quantum many-body wavefunctions is described, which we have termed qubism. Its main property is its recursivity: increasing the number of qubits reflects in an increase in the image resolution. Thus, the plots are typically fractal. As examples, we provide images for the ground states of commonly used Hamiltonians in condensed matter and cold atom physics, such as Heisenberg or ITF. Many features of the wavefunction, such as magnetization, correlations and criticality, can be visualized as properties of the images. In particular, factorizability can be easily spotted, and a way to estimate the entanglement entropy from the image is provided

How does bond percolation happen in coloured networks?

Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial transformations that include a phase transition in the connectivity, and in some special cases, multiple phase transitions. Here we establish a generic analytic theory that describes how structure and sizes of all connected components in the network are affected by simple and colour-dependant bond percolations. This theory predicts all locations where the phase transitions take place, existence of wide critical windows that do not vanish in the thermodynamic limit, and a peculiar phenomenon of colour switching that occurs in small connected components. These results may be used to design percolation-like processes with desired properties, optimise network response to percolation, and detect subtle signals that provide an early warning of a network collapse

Innovation and failure in mechatronics design education

Innovative engineering design always has associated with it the risk of failure, and it is the role of the design engineer to mitigate the possibilities of failure in the final system. Education should however provide a safe space for students to both innovate and to learn about and from failures. However, pressures on course designers and students can result in their adopting a conservative, and risk averse, approach to problem solving. The paper therefore considers the nature of both innovation and failure, and looks at how these might be effectively combined within mechatronics design education

Duality approach to one-dimensional degenerate electronic systems

We investigate the possible classification of zero-temperature spin-gapped phases of multicomponent electronic systems in one spatial dimension. At the heart of our analysis is the existence of non-perturbative duality symmetries which emerge within a low-energy description. These dualities fall into a finite number of classes that can be listed and depend only on the algebraic properties of the symmetries of the system: its physical symmetry group and the maximal continuous symmetry group of the interaction. We further characterize possible competing orders associated to the dualities and discuss the nature of the quantum phase transitions between them. Finally, as an illustration, the duality approach is applied to the description of the phases of two-leg electronic ladders for incommensurate filling.Comment: 53 pages, 3 figures, published versio

The density-matrix renormalization group

The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly acquired the status of method of choice for numerical studies of one-dimensional quantum systems. Its applications to the calculation of static, dynamic and thermodynamic quantities in such systems are reviewed. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and non-equilibrium statistical physics, and time-dependent phenomena is discussed. This review also considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by DMRG.Comment: accepted by Rev. Mod. Phys. in July 2004; scheduled to appear in the January 2005 issu

Quantum Fields on Star Graphs with Bound States at the Vertex

We investigate the propagation of a massless scalar field on a star graph, modeling the junction of $n$ quantum wires. The vertex of the graph is represented by a point-like impurity (defect), characterized by a one-body scattering matrix. The general case of off-critical scattering matrix with bound and/or antibound states is considered. We demonstrate that the contribution of these states to the scalar field is fixed by causality (local commutativity), which is the key point of our investigation. Two different regimes of the theory emerge at this stage. If bound sates are absent, the energy is conserved and the theory admits unitary time evolution. The behavior changes if bound states are present, because each such state generates a kind of damped harmonic oscillator in the spectrum of the field. These oscillators lead to the breakdown of time translation invariance. We study in both regimes the electromagnetic conductance of the Luttinger liquid on the quantum wire junction. We derive an explicit expression for the conductance in terms of the scattering matrix and show that antibound and bound states have a different impact, giving raise to oscillations with exponentially damped and growing amplitudes respectively.Comment: LaTex 1+29 pages, 2 figures: Expanded version with new title and abstract; clarifying comments, fig.2 and references added; final version to appear in J. Math. Phy

A Monte Carlo study of the triangular lattice gas with the first- and the second-neighbor exclusions

We formulate a Swendsen-Wang-like version of the geometric cluster algorithm. As an application,we study the hard-core lattice gas on the triangular lattice with the first- and the second-neighbor exclusions. The data are analyzed by finite-size scaling, but the possible existence of logarithmic corrections is not considered due to the limited data. We determine the critical chemical potential as $\mu_c=1.75682 (2)$ and the critical particle density as $\rho_c=0.180(4)$. The thermal and magnetic exponents $y_t=1.51(1) \approx 3/2$ and $y_h=1.8748 (8) \approx 15/8$, estimated from Binder ratio $Q$ and susceptibility $\chi$, strongly support the general belief that the model is in the 4-state Potts universality class. On the other hand, the analyses of energy-like quantities yield the thermal exponent $y_t$ ranging from $1.440(5)$ to $1.470(5)$. These values differ significantly from the expected value 3/2, and thus imply the existence of logarithmic corrections.Comment: 4 figures 2 table

Re-use of tests and arguments for assesing dependable mixed-critically systems

The safety assessment of mixed-criticality systems (MCS) is a challenging activity due to system heterogeneity, design constraints and increasing complexity. The foundation for MCSs is the integrated architecture paradigm, where a compact hardware comprises multiple execution platforms and communication interfaces to implement concurrent functions with different safety requirements. Besides a computing platform providing adequate isolation and fault tolerance mechanism, the development of an MCS application shall also comply with the guidelines defined by the safety standards. A way to lower the overall MCS certification cost is to adopt a platform-based design (PBD) development approach. PBD is a model-based development (MBD) approach, where separate models of logic, hardware and deployment support the analysis of the resulting system properties and behaviour. The PBD development of MCSs benefits from a composition of modular safety properties (e.g. modular safety cases), which support the derivation of mixed-criticality product lines. The validation and verification (V&V) activities claim a substantial effort during the development of programmable electronics for safety-critical applications. As for the MCS dependability assessment, the purpose of the V&V is to provide evidences supporting the safety claims. The model-based development of MCSs adds more V&V tasks, because additional analysis (e.g., simulations) need to be carried out during the design phase. During the MCS integration phase, typically hardware-in-the-loop (HiL) plant simulators support the V&V campaigns, where test automation and fault-injection are the key to test repeatability and thorough exercise of the safety mechanisms. This dissertation proposes several V&V artefacts re-use strategies to perform an early verification at system level for a distributed MCS, artefacts that later would be reused up to the final stages in the development process: a test code re-use to verify the fault-tolerance mechanisms on a functional model of the system combined with a non-intrusive software fault-injection, a model to X-in-the-loop (XiL) and code-to-XiL re-use to provide models of the plant and distributed embedded nodes suited to the HiL simulator, and finally, an argumentation framework to support the automated composition and staged completion of modular safety-cases for dependability assessment, in the context of the platform-based development of mixed-criticality systems relying on the DREAMS harmonized platform.La dificultad para evaluar la seguridad de los sistemas de criticidad mixta (SCM) aumenta con la heterogeneidad del sistema, las restricciones de diseño y una complejidad creciente. Los SCM adoptan el paradigma de arquitectura integrada, donde un hardware embebido compacto comprende múltiples plataformas de ejecución e interfaces de comunicación para implementar funciones concurrentes y con diferentes requisitos de seguridad. Además de una plataforma de computación que provea un aislamiento y mecanismos de tolerancia a fallos adecuados, el desarrollo de una aplicación SCM además debe cumplir con las directrices definidas por las normas de seguridad. Una forma de reducir el coste global de la certificación de un SCM es adoptar un enfoque de desarrollo basado en plataforma (DBP). DBP es un enfoque de desarrollo basado en modelos (DBM), en el que modelos separados de lógica, hardware y despliegue soportan el análisis de las propiedades y el comportamiento emergente del sistema diseñado. El desarrollo DBP de SCMs se beneficia de una composición modular de propiedades de seguridad (por ejemplo, casos de seguridad modulares), que facilitan la definición de líneas de productos de criticidad mixta. Las actividades de verificación y validación (V&V) representan un esfuerzo sustancial durante el desarrollo de aplicaciones basadas en electrónica confiable. En la evaluación de la seguridad de un SCM el propósito de las actividades de V&V es obtener las evidencias que apoyen las aseveraciones de seguridad. El desarrollo basado en modelos de un SCM incrementa las tareas de V&V, porque permite realizar análisis adicionales (por ejemplo, simulaciones) durante la fase de diseño. En las campañas de pruebas de integración de un SCM habitualmente se emplean simuladores de planta hardware-in-the-loop (HiL), en donde la automatización de pruebas y la inyección de faltas son la clave para la repetitividad de las pruebas y para ejercitar completamente los mecanismos de tolerancia a fallos. Esta tesis propone diversas estrategias de reutilización de artefactos de V&V para la verificación temprana de un MCS distribuido, artefactos que se emplearán en ulteriores fases del desarrollo: la reutilización de código de prueba para verificar los mecanismos de tolerancia a fallos sobre un modelo funcional del sistema combinado con una inyección de fallos de software no intrusiva, la reutilización de modelo a X-in-the-loop (XiL) y código a XiL para obtener modelos de planta y nodos distribuidos aptos para el simulador HiL y, finalmente, un marco de argumentación para la composición automatizada y la compleción escalonada de casos de seguridad modulares, en el contexto del desarrollo basado en plataformas de sistemas de criticidad mixta empleando la plataforma armonizada DREAMS.Kritikotasun nahastuko sistemen segurtasun ebaluazioa jarduera neketsua da beraien heterogeneotasuna dela eta. Sistema hauen oinarria arkitektura integratuen paradigman datza, non hardware konpaktu batek exekuzio plataforma eta komunikazio interfaze ugari integratu ahal dituen segurtasun baldintza desberdineko funtzio konkurrenteak inplementatzeko. Konputazio plataformek isolamendu eta akatsen aurkako mekanismo egokiak emateaz gain, segurtasun arauek definituriko jarraibideak jarraitu behar dituzte kritikotasun mistodun aplikazioen garapenean. Sistema hauen zertifikazio prozesuaren kostua murrizteko aukera bat plataformetan oinarritutako garapenean (PBD) datza. Garapen planteamendu hau modeloetan oinarrituriko garapena da (MBD) non modeloaren logika, hardware eta garapen desberdinak sistemaren propietateen eta portaeraren aurka aztertzen diren. Kritikotasun mistodun sistemen PBD garapenak etekina ateratzen dio moduluetan oinarrituriko segurtasun propietateei, adibidez: segurtasun kasu modularrak (MSC). Modulu hauek kritikotasun mistodun produktu-lerroak ere hartzen dituzte kontutan. Berifikazio eta balioztatze (V&V) jarduerek esfortzu kontsideragarria eskatzen dute segurtasun-kiritikoetarako elektronika programagarrien garapenean. Kritikotasun mistodun sistemen konfiantzaren ebaluazioaren eta V&V jardueren helburua segurtasun eskariak jasotzen dituzten frogak proportzionatzea da. Kritikotasun mistodun sistemen modelo bidezko garapenek zeregin gehigarriak atxikitzen dizkio V&V jarduerari, fase honetan analisi gehigarriak (hots, simulazioak) zehazten direlako. Bestalde, kritikotasun mistodun sistemen integrazio fasean, hardware-in-the-loop (Hil) simulazio plantek V&V iniziatibak sostengatzen dituzte non testen automatizazioan eta akatsen txertaketan funtsezko jarduerak diren. Jarduera hauek frogen errepikapena eta segurtasun mekanismoak egiaztzea ahalbidetzen dute. Tesi honek V&V artefaktuen berrerabilpenerako estrategiak proposatzen ditu, kritikotasun mistodun sistemen egiaztatze azkarrerako sistema mailan eta garapen prozesuko azken faseetaraino erabili daitezkeenak. Esate baterako, test kodearen berrabilpena akats aurkako mekanismoak egiaztatzeko, modelotik X-in-the-loop (XiL)-ra eta kodetik XiL-rako konbertsioa HiL simulaziorako eta argumentazio egitura bat DREAMS Europear proiektuan definituriko arkitektura estiloan oinarrituriko segurtasun kasu modularrak automatikoki eta gradualki sortzeko