Exploring neural network training strategies to determine phase transitions in frustrated magnetic models Autores:Corte, Inés Raquel Acevedo, Santiago Daniel Arlego, Marcelo José Fabián Lamas, Carlos Alberto Fecha: 2021-01-01Tipo de documento: ArticuloResumen:The transfer learning of a neural network is one of its most outstanding aspects and has given supervised learning with neural networks a prominent place in data science. Here we explore this feature in the context of strongly interacting many-body systems. Through case studies, we test the potential of this deep learning technique to detect phases and their transitions in frustrated spin systems, using fully-connected and convolutional neural networks. In addition, we explore a recently-introduced technique, which is at the middle point of supervised and unsupervised learning. It consists in evaluating the performance of a neural network that has been deliberately “confused” during its training. To properly demonstrate the capability of the “confusion” and transfer learning techniques, we apply them to a paradigmatic model of frustrated magnetism in two dimensions, to determine its phase diagram and compare it with high-performance Monte Carlo simulations.Compartir:
Phase diagram study of a two-dimensional frustrated antiferromagnet via unsupervised machine learning Fecha: 2021-01-01Tipo de documento: PreprintResumen:We apply unsupervised learning techniques to classify the different phases of the J₁-J₂ antiferromagnetic Ising model on the honeycomb lattice. We construct the phase diagram of the system using convolutional autoencoders. These neural networks can detect phase transitions in the system via "anomaly detection'' without the need for any label or a priori knowledge of the phases. We present different ways of training these autoencoders, and we evaluate them to discriminate between distinct magnetic phases. In this process, we highlight the case of high-temperature or even random training data. Finally, we analyze the capability of the autoencoder to detect the ground state degeneracy through the reconstruction error.Compartir:
Magnon crystals and magnetic phases in a Kagomé-stripe antiferromagnet Fecha: 2019-01-01Tipo de documento: PreprintResumen:In this paper we analyze the magnetization properties of an antiferromagnetic kagome-stripe lattice, motivated by the recent synthesis of materials exhibiting this structure. By employing a variety of techniques that include numerical methods such as density-matrix renormalization-group and Monte Carlo simulations, as well as analytical techniques such as perturbative low-energy effective models and exact solutions, we characterize the magnetization process and magnetic phase diagram of a kagome-stripe lattice. The model captures a variety of behaviors present in the two-dimensional kagome lattice, which are described here by analytical models and numerically corroborated. In addition to the characterization of semiclassical intermediate plateaus, it is worth noting the determination of an exact magnon crystal phase which breaks the underlying symmetry of the lattice. This magnon crystal phase generalizes previous findings.Compartir:
Teaching Basic Special Relativity in High School: The Role of Classical Kinematics Fecha: 2017-11-01Tipo de documento: ArticuloResumen:In this work, we present a possible didactic sequence for the study of basic aspects of special relativity in high school. The sequence re-signifies the role of classical kinematics and Galileo´s relativity principle. It has been implemented in four courses of two secondary schools in Argentina in 2014-2015 and in Colombia in 2016, with students aged 15-16, during 20 school hours, being the teacher a member of our research team.Compartir:
Magnetization process in a frustrated plaquette dimer Fecha: 2017-06-30Tipo de documento: ArticuloResumen:The magnetic phase diagram of a plaquette dimerized and frustrated antiferromagnetic ladder system is studied by using a combination of numerical and analytical techniques. For the strongly frustrated regime, series expansions and bond operator techniques are employed to analyze zero magnetic field, whereas low-energy effective models are used to study the complete magnetization process. The interplay between frustration and dimerization gives rise to a rich plateau structure that is captured by effective models and corroborated by numerical density matrix renormalization group simulations, in particular, the emergence of intermediate plateaus at M=14 and 34 of saturation in the magnetization curve is clarified.Compartir:
Light and matter diffraction from the unified viewpoint of Feynman's Sum of all Paths Fecha: 2017-06-01Tipo de documento: ArticuloResumen:In this work, we present a pedagogical strategy to describe the diffraction phenomenon based on a didactic adaptation of the Feynman's path integrals method, which uses only high school mathematics. The advantage of our approach is that it allows to describe the diffraction in a fully quantum context, where superposition and probabilistic aspects emerge naturally. Our method is based on a time-independent formulation, which allows modelling the phenomenon in geometric terms and trajectories in real space, which is an advantage from the didactic point of view. A distinctive aspect of our work is the description of the series of transformations and didactic transpositions of the fundamental equations that give rise to a common quantum framework for light and matter. This is something that is usually masked by the common use, and that to our knowledge has not been emphasized enough in a unified way. Finally, the role of the superposition of nonclassical paths and their didactic potential are briefly mentioned.Compartir:
Fases cuánticas y degeneración clásica en un antiferromagneto cuántico sobre la red de panal de abejas de dos capas Fecha: 2017-01-01Tipo de documento: Objeto de conferenciaResumen:En este trabajo estudiamos la evolución de una fase de dímeros cuánticos sobre la red de tipo panal de abejas utilizando una representación de los operadores de espín en términos de operadores bosónicos. Este modelo ha sido propuesto para describir las propiedades del material Bi3Mn4012(N03), por lo que el presente estudio puede ser relevante para describir el magnetismo de este material y otros con características similares. Llevando a cabo un desacoplamiento de campo medio, calculamos la relación de dispersión y a partir de la misma determinamos el gap de espín. Interesantemente, aunque el cierre de gap es calculado en un modelo puramente cuántico, éste ocurre sobre una curva continua en el espacio de momentos que coincide con la variedad de estados clásicos de mínima energía, In this work, we study the evolution of a quantum dimer phase over the honeycomb bilayer lattice using a representation of the spins in terms of bosonic operators. This model has been proposed to describe the properties of the material Bi3Mn4012(N03), so the present study may be relevant to describe the magnetism in this compound and materials with similar characteristics. Performing a mean field decoupling, we calculate the dispersion relation and determine the spin gap. Interestingly, although the gap closure calculation is based on a purely quantum model, it occurs on a continuous curve in the momentum space that coincides with the variety of classical states of minimum energy.Compartir:
Fases cuánticas y degeneración clásica en un antiferromagneto cuántico sobre la red de panal de abejas de dos capas Fecha: 2017-01-01Tipo de documento: Objeto de conferenciaResumen:En este trabajo estudiamos la evolución de una fase de dímeros cuánticos sobre la red de tipo panal de abejas utilizando una representación de los operadores de espín en términos de operadores bosónicos. Este modelo ha sido propuesto para describir las propiedades del material Bi3Mn4O12(NO3), por lo que el presente estudio puede ser relevante para describir el magnetismo de este material y otros con características similares. Llevando a cabo un desacoplamiento de campo medio, calculamos la relación de dispersión y a partir de la misma determinamos el gap de espín. Interesantemente, aunque el cierre de gap es calculado en un modelo puramente cuántico, éste ocurre sobre una curva continua en el espacio de momentos que coincide con la variedad de estados clásicos de mínima energía.Compartir:
Quantum phase diagram of a frustrated antiferromagnet on the bilayer honeycomb lattice Fecha: 2016-06-27Tipo de documento: ArticuloResumen:We study the spin-1/2 Heisenberg antiferromagnet on a bilayer honeycomb lattice including interlayer frustration. Using a set of complementary approaches, namely, Schwinger bosons, dimer series expansion, bond operators, and exact diagonalization, we map out the quantum phase diagram. Analyzing ground-state energies and elementary excitation spectra, we find four distinct phases, corresponding to three collinear magnetic long-range ordered states, and one quantum disordered interlayer dimer phase. We detail that the latter phase is adiabatically connected to an exact singlet product ground state of the bilayer, which exists along a line of maximum interlayer frustration. The order within the remaining three phases will be clarified.Compartir:
Co-disciplinary Physics and Mathematics Research and Study Course (RSC) within three study groups: teachers-in-training, secondary school students and researchers Autores:Otero, María Rita Gazzola Bascougnet, María Paz Llanos, Viviana Carolina Arlego, Marcelo José Fabián Fecha: 2016-01-01Tipo de documento: ArticuloResumen:This work shows the results of a research carried out in secondary school and university developing a co-disciplinary Research and Study Course (RSC) on questions connected to Physics and Mathematics in different groups. We present preliminary results of the RSC developed in three different groups: science education researchers, N=25 Mathematics teacher students (training teachers of Mathematics) at University, and N= 68 secondary school students. The development and scope of the RSC in each group is described by using the RSC components as defined by Chevallard's Anthropological Theory of the Didactic (ATD) (2012). Furthermore, a short description of the Praxeological Model of Reference is presented. This model was built by the researchers group in order to reply to the generative question, unknown in the beginning, and to anticipate and to conceive the evolution of the possible SRC in each institution. Some general results in each group are discussed and some conclusions concerning the ecology of the pedagogy of research and questioning the world at university and secondary schools are drawn.Compartir:
Enseñanza y aprendizaje de aspectos fundamentales de física cuántica en la escuela secundaria a partir del estudio de la luz Fecha: 2016-01-01Tipo de documento: Objeto de conferenciaResumen:En este trabajo se presenta un análisis de la evaluación que realizaron los estudiantes de cuatro cursos de escuelas secundarias (N=83), al final de la implementación de una secuencia de situaciones relativa a la luz, que adopta el enfoque de la “Suma de Caminos Alternativos” de Feynman para abordar su aspecto cuántico. Las respuestas de los estudiantes fueron categorizadas según sus obstáculos y avances en la conceptualización Se generaron seis grupos que representan sendos estados de conceptualización, que permiten explicar el aprendizaje de la totalidad de los estudiantes de este trabajo. El análisis, realizado en base a la Teoría de los Campos Conceptuales de Vergnaud, permitió identificar un conjunto de posibles teoremas en acto utilizados por los estudiantes para afrontar las situaciones relativas a las nociones cuánticas presentadas en la secuencia de situaciones.Compartir:
Análisis de la conceptualización en la fase de predicción y experimentación de una enseñanza de aspectos cuánticos de la luz basada en el enfoque de Feynman Fecha: 2016-01-01Tipo de documento: Objeto de conferenciaResumen:En este trabajo se presenta la primera parte de un conjunto de situaciones que componen una secuencia diseñada para enseñar conceptos relativos a la luz, que enfatizan su aspecto cuántico, con el fin de promover su conceptualización en estudiantes del último año de la escuela secundaria. Comenzar la secuencia de situaciones con este conjunto de experiencias con luz (en su mayoría realizables en el aula de clases) es muy importante porque establece la necesidad de contar con una formulación de una explicación cuántica y unificada de las mismas, que en este caso es el enfoque de Caminos Múltiples de Feynman. Se presenta un análisis de la conceptualización, basada en la Teoría de los Campos Conceptuales de Vergnaud de los N=83 estudiantes que participaron en la implementación.Compartir:
Teaching the basic concepts of the Special Relativity in the secondary school in the framework of the Theory of Conceptual Fields of Vergnaud Fecha: 2015-05-01Tipo de documento: ArticuloResumen:In this work, we investigate the conceptualization of the basic aspects of Special Relativity (SR) at secondary school level. We have conducted our research along the lines of the Theory of Conceptual Fields (TCF) proposed by Vergnaud (Vergnaud G., Infancia y Aprendizaje, 36 (2013) 131). The investigation consisted in the design, implementation and evaluation of a didactic sequence specially elaborated to conceptualize the basic aspects of SR. The proposal is composed by eight situations, complemented with a set of exercises. It was carried out in two classrooms with students of the last year of secondary level (17 years old, N = 43). The conceptualization was analyzed in a classroom context, where the selected situations are essential to promote the emergence of the relevant concepts.Compartir:
Design, analysis and reformulation of a didactic sequence for teaching the special theory of relativity in high school Fecha: 2015-01-01Tipo de documento: ArticuloResumen:In this work, we design, implement and analyze a didactic sequence for the teaching of the basic topics of special relativity theory in high school. The sequence proposes a series of situations, specially designed to allow the emergence of the central aspects of special relativity. The conceptualization process is investigated from the point of view of the theory of conceptual fields of Vergnaud. By means of a careful analysis of classroom student productions we detect the key theorems-in-action they use, evidencing that most of conceptual errors are of pre-relativistic nature. This leads us to a reformulation of the sequence, which promotes the conceptualization of Galilean relativity and the principles of the special relativity. This previous step aims at bringing to students a firm basis to address the more complex aspects of the subject.Compartir:
Las dialécticas en un Recorrido de Estudio e Investigación para la enseñanza del cálculo vectorial en la universidad Fecha: 2015-01-01Tipo de documento: ArticuloResumen:En este trabajo se presenta un análisis didáctico relativo a un Recorrido de Estudio e Investigación (REI) para el estudio del Cálculo Vectorial, considerando las dialécticas propuestas por la Teoría Antropológica de lo Didáctico (TAD). El REI se desarrolló en un curso de matemática en una Facultad de Ingeniería en el marco de la Pedagogía de la Investigación y del Cuestionamiento del Mundo (PICM). In this paper a didactic analysis related to a Research and Study Path (RSP) for the study of Vector Calculus, considering the dialectics proposed by the Anthropologic Theory of the Didactic (ATD) is presented. The RSP was developed in a mathematics course in a Faculty of Engineering under the Pedagogy of the Research and Questioning the World (PRQW).Compartir:
Self consistent study of the quantum phases in a frustrated antiferromagnet on the bilayer honeycomb lattice Fecha: 2014-12-08Tipo de documento: ArticuloResumen:We study the frustrated Heisenberg model on the bilayer honeycomb lattice. The ground-state energy and spin gap are calculated, using different bosonic representations at mean field level and numerical calculations, to explore different sectors of the phase diagram. In particular we make use of a bond operator formalism and series expansion calculations to study the extent of dimer inter-layer phase. On the other hand we use the Schwinger boson method and exact diagonalization on small systems to analyze the evolution of on-layer phases. In this case we specifically observe a phase that presents a spin gap and short range Neel correlations that survives even in the presence of non-zero next-nearest-neighbor interaction and inter-layer coupling.Compartir:
Magnetization plateaux and jumps in frustrated four-leg spin tubes in magnetic fields Fecha: 2014-12-08Tipo de documento: Objeto de conferenciaResumen:We study the ground state phase diagram of a frustrated spin-1/2 four-leg tube in an external magnetic field. We explore the parameter space of this model in the regime of all-antiferromagnetic exchange couplings by means of three different approaches: density matrix renormalization group (DMRG), a low-energy effective Hamiltonian (LEH) and a Hartree variational approach (HVA). We find that in the limit of weakly interacting plaquettes, singlet and triplet states play an important role in the formation of magnetization plateaux. We study the transition regions numerically and analytically, and find that they are described, at first order in a strong- coupling expansion, by an XXZ spin-1/2 chain in a magnetic field. These results are consistent with the DMRG and HVA calculations.Compartir:
The double slit experience with light from the point of view of Feynman's sum of multiple paths Fecha: 2014-05-01Tipo de documento: ArticuloResumen:This paper presents an analysis of the double slit experience with light, by using concepts of the Feynman method of “sum of multiple paths” in quantum mechanics. The advantages of this formulation for the teaching of basic aspects of quantum mechanics in the high-school level are analyzed. Este trabalho apresenta uma análise da experiência de fenda dupla com luz, utilizando conceitos do método de “Soma de vários caminhos” da formulação de Feynman da mecânica quântica. São analisadas as vantagens desta formulação para o ensino no nível médio de aspectos básicos da mecânica quântica.Compartir:
Quantum phases in the frustrated Heisenberg model on the bilayer honeycomb lattice Fecha: 2014-01-06Tipo de documento: PreprintResumen:We use a combination of analytical and numerical techniques to study the phase diagram of the frustrated Heisenberg model on the bilayer honeycomb lattice. Using the Schwinger-boson description of the spin operators followed by a mean-field decoupling, the magnetic phase diagram is studied as a function of the frustration coupling J2 and the interlayer coupling J⊥. The presence of both magnetically ordered and disordered phases is investigated by means of the evaluation of ground-state energy, spin gap, local magnetization, and spin-spin correlations. We observe a phase with a spin gap and short-range Néel correlations that survives for nonzero next-nearest-neighbor interaction and interlayer coupling. Furthermore, we detect signatures of a reentrant behavior in the melting of the Néel phase and symmetry restoring when the system undergoes a transition from an on-layer nematic valence-bond crystal phase to an interlayer valence-bond crystal phase. We complement our work with exact diagonalization on small clusters and dimer-series expansion calculations, together with a linear spin-wave approach to study the phase diagram as a function of the spin S, the frustration, and the interlayer couplings.Compartir:
Enseñanza del cálculo vectorial en la universidad: propuesta de recorridos de estudio e investigación Fecha: 2014-01-01Tipo de documento: ArticuloResumen:En este trabajo realizamos una propuesta para la enseñanza del Cálculo Vectorial en el contexto de una Facultad de Ingeniería mediante el dispositivo didáctico llamado Recorridos de Estudio e Investigación (REI). Este dispositivo ha sido propuesto por Chevallard en el marco de la Teoría Antropológica de lo Didáctico (TAD), que plantea una enseñanza bajo el paradigma de la pedagogía de la investigación y del cuestionamiento del mundo. Analizamos las condiciones que facilitarían y las que obstaculizarían la ecología del REI en esa institución e introducimos el modelo praxeológico de referencia. Finalmente presentamos una descripción de la implementación del REI y un análisis preliminar de las organizaciones matemáticas que surgieron en el mismo. In this work we elaborate a proposal for vector calculus teaching in the context of a Faculty of Engineering by means of the teaching device called Trajectories of Study and Research (TEI). This device has been introduced by Chevallard in the framework of Anthropological Theory of Didactics (ATD), which proposes a teaching under the paradigm of pedagogy of research and questioning the world. We analyze the conditions that facilitate and those that hamper TEI ecology in that institution and introduce the reference praxeological model. Finally we present a description of REI implementation and a preliminary analysis of mathematical organizations that emerged after its implementation.Compartir:
El rol de la historia de las ciencias en la enseñanza del Cálculo Vectorial en carreras de Ingeniería Fecha: 2013-12-01Tipo de documento: ArticuloResumen:En este trabajo presentamos una posible estrategia didáctica para la enseñanza del Cálculo Vectorial en carreras de Ingeniería. La misma aborda una perspectiva histórica, contextualizando los conceptos matemáticos con el conjunto de fenómenos físicos que motivaron su origen. Para ello, exponemos una reseña de los orígenes del Cálculo Vectorial durante los siglos XVIII y XIX. Se consideran reflexiones de investigadores enfatizando la importancia de incorporar aspectos epistemológicos e historiográficos, en la enseñanza de las ciencias. In this work we present a possible didactic strategy for teaching vector calculus in engineering careers. It addresses a historical perspective, contextualizing mathematical concepts with physical phenomena that led to its origin. To this end, we present an overview of the origin of vector calculus during the eighteenth and nineteenth centuries. We consider reflections of researchers emphasizing the importance of incorporating epistemological and historiographical aspects in science education. Neste trabalho apresentamos uma possível estratégia didática para o ensino de cálculo vetorial em carreiras de engenharia. Ele aborda uma perspectiva histórica, contextualizando os conceitos matemáticos com fenômenos físicos que levaram à sua origem. Para este fim, apresentamos uma visão geral da origem do cálculo vetorial, durante os séculos XVIII e XIX. Finalmente, consideramos as reflexões de pesquisadores, enfatizando a importância de incorporar aspectos epistemológicos e historiográficos em educação científica.Compartir:
Scaling and width distributions of parity-conserving interfaces Fecha: 2013-09-01Tipo de documento: ArticuloResumen:We present an alternative finite-size approach to a set of parity-conserving interfaces involving attachment, dissociation, and detachment of extended objects in 1+1 dimensions. With the aid of a nonlocal construct introduced by Barma and Dhar in related systems [Phys. Rev. Lett. 73, 2135 (1994)], we circumvent the subdiffusive dynamics and examine close-to-equilibrium aspects of these interfaces by assembling states of much smaller, numerically accessible scales. As a result, roughening exponents, height correlations, and width distributions exhibiting universal scaling functions are evaluated for interfaces virtually grown out of dimers and trimers on large-scale substrates. Dynamic exponents are also studied by finite-size scaling of the spectrum gaps of evolution operators.Compartir:
Quantum phases of a frustrated four-leg spin tube Autores:Arlego, Marcelo José Fabián Brenig, Wolfram Rahnavard, Yousef Willenberg, B. Rosales, Héctor Diego Rossini, Gerardo Luis Fecha: 2013-01-09Tipo de documento: PreprintResumen:We study the ground state phase diagram of a frustrated spin-1/2 four-leg tube. Using a variety of complementary techniques, namely density matrix renormalization group, exact diagonalization, Schwinger boson mean field theory, quantum Monte-Carlo and series expansion, we explore the parameter space of this model in the regime of all-antiferromagnetic exchange. In contrast to unfrustrated four-leg tubes we uncover a rich phase diagram. Apart from the Luttinger liquid fixed point in the limit of decoupled legs, this comprises several gapped ground states, namely a plaquette, an incommensurate, and an antiferromagnetic quasi spin-2 chain phase. The transitions between these phases are analyzed in terms of total energy and static structure factor calculations and are found to be of (weak) first order. Despite the absence of long range order in the quantum case, remarkable similarities to the classical phase diagram are uncovered, with the exception of the icommensurate regime, which is strongly renormalized by quantum fluctuations. In the limit of large leg exchange the tube exhibits a deconfinement cross-over from gapped magnon like excitations to spinons.Compartir:
A proposal to teach light in a unified framework using the Feynman method Fecha: 2012-06-01Tipo de documento: ArticuloResumen:The goal of this proposal is to teach the basic aspects of light from the point of view of quantum mechanics at high school level. To this end, we have adapted Feynman´s Path Integral Method of Quantum Mechanics. This is a continuation of previous works where we considered the quantum behaviour of matter. The situations were to promote the conceptualization of the electron as a quantum system, the probabilistic function and the transition quantum-classic. Now, the goal is to build a new proposal to teach the behaviour of the light from an actual vision and from a unified model: the quantum mechanics, from the reconstruction of a reference that also uses the approach Path Integrals of Richard Feynman. It is adapted for secondary school students using vectors and sums, and it is inserted in a problems context about the light. Careful and accurate language is used, avoiding terms like photon or expressions likeparticles of light or wave-particle duality, because these ideas could present obstacles to understanding key aspects of quantum theory. This proposal is an alternative to avoid historical approaches commonly used so far and it is being implemented in two groups of students in secondary school (15-16 years old).Compartir:
Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman's Path Integrals Method Fecha: 2012-03-01Tipo de documento: ArticuloResumen:This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman’s path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. We start by discussing the experimental results that would be observed in an idealized double-slit experiment. With the assistance of software simulations, we focus on the changes observed as the objects’ masses are reduced from macroscopic to atomic values. After that we introduce the basis of quantum mechanics by means of the concepts of path integrals, which henceforth we will call “sum of all alternatives.” Finally, we show how the transition from classical to quantum behavior naturally emerges within the framework of “sum of all alternatives.”Compartir:
Quantum phases of the planar antiferromagnetic J₁-J₂-J₃ Heisenberg model Autores:Reuther, Johannes Wölfle, Peter Darradi, Rachid Brenig, Wolfram Arlego, Marcelo José Fabián Richter, Johannes Fecha: 2011-02-01Tipo de documento: ArticuloResumen:We present results for a complementary analysis of the frustrated planar J₁-J₂-J₃ spin-1/2 quantum antiferromagnet (AFM). Using dynamical functional renormalization group, high-order-coupled cluster calculations, and series expansion based on the flow equation method, we have calculated generalized momentum-resolved susceptibilities, the ground-state energy, the magnetic-order parameter, and the elementary excitation gap. From these, we determine a quantum phase diagram that shows a large window of a quantum paramagnetic (QP) phase situated among the Néel, spiral, and collinear states, which are present already in the classical J₁-J₂-J₃ AFM. Our findings are consistent with substantial plaquette correlations in the QP phase. The extent of the QP region is found to be in satisfying agreement between the three different approaches we have employed.Compartir:
Series expansion analysis of a frustrated four-spin tube Fecha: 2011-01-01Tipo de documento: ArticuloResumen:We study the magnetism of a frustrated four-leg spin-1/2 ladder with transverse periodic boundary conditions: the frustrated four-spin tube (FFST). Using a combination of series expansion (SE), based on the continuous unitary transformation method and density-matrix renormalization group (DMRG) we analyze the ground-state, the one-, and the two-particle excitations in the regime of strong rung coupling. We find several marked differences of the FFST with respect to standard two-leg ladders. First, we show that frustration destabilizes the spin-gap phase of the FFST, which is adiabatically connected to the limit of decoupled rung singlets, leading to a first-order quantum phase transition at finite interrung coupling. Second, we show that apart from the well-known triplon branch of spin ladders, the FFST sustains additional elementary excitations, including a singlon and additional triplons. Finally, we find that in the two-particle sector, the FFST exhibits collective (anti)bound states similar to two-leg ladders, however, with a different ordering of the spin-quantum numbers. We show that frustration has significant impact on the FFST leading to a flattening of the ground-state energy landscape, a mass-enhancement of the excitations, and to a relative enhancement of the (anti)binding strength. Where possible, we use DMRG to benchmark the findings from our SE calculations, showing excellent agreement.Compartir:
Tratamiento de la naturaleza de la luz en los libros de texto: un análisis crítico Fecha: 2011-01-01Tipo de documento: Objeto de conferenciaResumen:Este trabajo está en la línea de las investigaciones previas y actuales relativas a la enseñanza de nociones fundamentales de Mecánica Cuántica en la escuela (Fanaro, Otero y Arlego, 2009,2010, Fanaro, Fanaro, Otero, Arlego, Elgue 2011). Aquí presentamos un análisis de cómo los libros de texto para la escuela secundaria y/o preuniversitaria tratan los modelos para la luz, desde una postura crítica.Compartir:
Enseñanza del cálculo vectorial en el contexto de la Ingeniería: una revisión bibliográfica Fecha: 2011-01-01Tipo de documento: Objeto de conferenciaResumen:En este trabajo se expone una revisión bibliográfica que se enmarca en la etapa inicial de una tesis de doctorado en la que se abordará la problemática de la enseñanza del cálculo vectorial en carreras de ingeniería. El objetivo de este trabajo es relevar las distintas estrategias de enseñanza que tienen como propósito ayudar al alumno en la vinculación y comprensión de los conceptos involucrados, identificar posibles encuadres teóricos y metodológicos y delimitar la relevancia del problema de investigación. Para ello se analizan libros, artículos en revistas científicas, de divulgación, actas de congresos, simposios y jornadas, que abordan la problemática mencionada.Compartir:
Enseñar el comportamiento de la luz en la escuela secundaria desde una visión actual utilizando el método de caminos múltiples de Feynman Fecha: 2011-01-01Tipo de documento: Objeto de conferenciaResumen:Este trabajo es una continuación de nuestros trabajos previos donde abordamos los aspectos cuánticos de la materia (Fanaro, Otero, y Arlego, 2009, 2010). Ahora nos ocupamos de los aspectos cuánticos de la luz. Aquí presentamos un análisis de los diferentes aspectos de la luz en un marco unificado, de forma no tradicional, que será el punto de partida de una propuesta didáctica para la Escuela Secundaria. En una primera etapa, presentamos un conjunto de fenómenos experimentales donde la luz exhibe en ciertos casos características que se asocian a comportamiento de partícula y en otras a un comportamiento ondulatorio. Luego presentamos experimentos donde la luz exhibe un carácter “especial”, es decir ni de onda, ni de partícula, sino algo esencialmente nuevo, sin análogo en el mundo macroscópico, denominado “comportamiento cuántico”. En una segunda etapa del trabajo mostramos cómo es posible explicar estos tres aspectos diferentes de la luz desde una única formulación, llamada “teoría cuántica de la luz”. Para esto emplearemos los conceptos de la formulación de “suma de caminos” de la mecánica cuántica. Nuestro abordaje enfatiza los aspectos conceptuales, reduciendo el contenido matemático al uso de vectores.Compartir:
Análisis de la conceptualización de un grupo de estudiantes de escuela secundaria al abordar situaciones de mecánica cuántica Fecha: 2011-01-01Tipo de documento: Objeto de conferenciaResumen:Presentamos una síntesis del trabajo de tesis que aborda el problema de la enseñanza de conceptos fundamentales de Mecánica Cuántica en la escuela media (Fanaro, 2009). Allí, elaboramos una estructura conceptual de referencia relacionada con el enfoque de la Mecánica Cuántica de Feynman “Path Integrals” o “Caminos Múltiples” adoptando los lineamientos didácticos propuestos en Otero (2006; 2007). Implementamos la propuesta en cursos de escuela media, y analizamos su viabilidad y adaptabilidad institucional. Presentamos aquí los resultados relativos a la conceptualización de los estudiantes, describiendo algunos teoremas y conceptos en acto que los estudiantes utilizaron al abordar las primeras situaciones planteadas en la secuencia.Compartir:
Teaching the foundations of quantum mechanics in secondary school: a proposed conceptual structure Fecha: 2009-01-01Tipo de documento: ArticuloResumen:This paper is part of a doctoral thesis that investigates Basic Quantum Mechanics (QM) teaching in high school. A Conceptual Structure of Reference (CSR) based on the Path Integral Method of Feynman (1965) was rebuilt and a Proposed Conceptual Structure for Teaching (PCST) (Otero, 2006, 2007) the basics of Quantum Mechanics at secondary school was designed, analysed and carried out. This PCST does not follow the historical route and it is complementary to the canonical formalism. The concepts: probability distribution, quantum system, x(t) alternative, amplitude of probability, sum of probability amplitude, action, Planck's constant, and classicquantum transition were rebuilt with the students. Mathematical formalism was avoided by using simulation software assistance. The Proposed Conceptual Structure for Teaching (PCST) is described and some results from the test carried out by the class group are discussed. This information allows the analysis of the Conceptual Structure Effectively Reconstructed (CSER) to be initiated with the students. Este trabajo es parte de una tesis doctoral que investiga la enseñanza de los fundamentos de la Mecánica Cuántica en la Escuela media. Se reconstruyó una estructura Conceptual de Referencia (ECR) basada en el método de la Integral de Camino de Feynman (1965) y se diseñó, analizó e implementó una Estructura Conceptual Propuesta para Enseñar (ECPE) (Otero, 2006, 2007) fundamentos de Mecánica Cuántica en la escuela media. Esta ECPE no sigue el camino histórico y es complementaria al formalismo canónico. Los conceptos: distribución de probabilidad, sistema cuántico, trayectoria alternativa x(t), amplitud de probabilidad, suma de amplitud de probabilidad acción, constante de Planck y transición clásica-cuántica se reconstruyeron con los estudiantes. Se describe la Estructura Conceptual Propuesta para Enseñar (ECPE) y se discuten algunos resultados de la evaluación realizada por el grupo de clase. Esta información permite el análisis de la Estructura Conceptual Efectivamente Reconstruida (ECER) con los estudiantes.Compartir:
Investigación y desarrollo de propuestas didácticas para la enseñanza de la Física en la escuela secundaria: Nociones cuánticas Fecha: 2009-01-01Tipo de documento: ArticuloResumen:En este trabajo se describe el proceso de desarrollo de una secuencia didáctica para enseñar conceptos fundamentales de Mecánica Cuántica en la Secundaria. Fundamentalmente se describe el referencial didáctico que se asume. Se definen las distintas estructuras conceptuales que es necesario reconstruir para abordar el problema de cómo enseñar nociones cuánticas partiendo de la situación del alumno, respetando su lugar e invitándolo a que asuma su responsabilidad, es decir, generando una dinámica emocional de aceptación. Se describe la Estructura Conceptual de Referencia que es definida por el investigador. El analiza las relaciones conceptuales que viven en la Comunidad Científica que genera el conocimiento y que tomará como referencia, y a la vez, la comunidad en la que ese saber va a ser reconstruido y las transformaciones que serán necesarias para enseñarlo. Se describe brevemente la Estructura Conceptual propuesta para enseñar y se discuten de manera general algunos resultados obtenidos en la implementación escolar de la ECPE con relación a la conceptualización y a la viabilidad de la secuencia. This paper describes the process of development of a didactical sequence to teach basic concepts of quantum mechanics in secondary school. Basically, the didactical framework adopted is described. The different conceptual structures that have to be developed to approach the problem of how to teach basic concepts of quantum mechanics starting from the student’s knowledge, respecting the student’s place (freedom) and inviting him to take his own responsibility, this implies creating an emotional dynamic of acceptance into the classroom. The Conceptual Structure of Reference that must be defined by the researcher is described. The researcher analyzes the conceptual relationships existing in the scientific community where knowledge is generated and that he will adopt as his frame of reference, also, he must take into account the community where that knowledge will be reconstructed and the knowledge transformations that will be necessary for teaching. Briefly, the Conceptual Structure Proposed to Teach is described and some results obtained during the scholar implementation of the CSPT, related to the conceptualization and viability of the sequence, are discussed in general.Compartir:
Los fundamentos de la mecánica cuántica en la escuela secundaria utilizando el concepto de integral de camino Autores:Arlego, Marcelo José Fabián Fecha: 2008-01-01Tipo de documento: ArticuloResumen:Analizamos las posibilidades de introducir las ideas básicas de la mecánica cuántica en la escuela secundaria, adaptando los conceptos de la formulación de integrales de camino (path integrals) para los estudiantes. Este trabajo focaliza en el fundamento teórico de la propuesta y en las adaptaciones necesarias para una posible implementación de esta en un curso del último año. We analyze the possibilities of introducing the basic ideas of quantum mechanics into secondary school, by adapting the path integral formulation’s concepts for the students. This work focuses on this proposal’s theoretical basis and what aspects of the formalism should be adapted in order to be implemented in the last year’s course.Compartir:
Software de simulación y reconstrucción de fundamentos de la mecánica cuántica en la escuela Fecha: 2007-01-01Tipo de documento: ArticuloResumen:Es difícil aceptar la posibilidad de estudiar conceptos de mecánica cuántica en la escuela secundaria, debido a su formalismo matemático por un lado, y a su imposibilidad de realizar experiencias cruciales que contextualicen ese saber, por el otro. Nuestra propuesta apunta a una forma posible de superar ambos obstáculos simultáneamente: implementar la técnica "Path Integrals" de Feynman, adaptada a los conocimientos de los estudiantes, apoyada en simulaciones donde se aplique la técnica y se pueda arribar a una descripción de los fundamentos del mundo microscópico (distribución de probabilidades). Como este trabajo forma parte de un trabajo de tesis en el que se propone, discute, y analiza una Estructura Conceptual para Estudiar (ECPE) los aspectos fundamentales de la mecánica cuántica en la escuela, lo que presentamos aquí es en primer lugar el modelo que aproxima las integrales de camino a sumas vectoriales, -de ahí el nombre Suma de Todas las Alternativas (STA)-. Luego, mostramos las simulaciones que creamos específicamente para la aplicación de la técnica, en el marco de nuestra ECPE.Compartir:
Bond-impurity induced bound states in disordered spin-1/2 ladders Autores:Arlego, Marcelo José Fabián Brenig, Wolfram Cabra, Daniel Carlos Heidrich-Meisner, Fabian Honecker, Andreas Rossini, Gerardo Luis Fecha: 2004-07-30Tipo de documento: ArticuloResumen:We discuss the effect of weak bond-disorder in two-leg spin ladders on the dispersion relation of the elementary triplet excitations with a particular focus on the appearance of bound states in the spin gap. Both the cases of modified exchange couplings on the rungs and the legs of the ladder are analyzed. Based on a projection on the single-triplet subspace, the single-impurity and small cluster problems are treated analytically in the strong-coupling limit. Numerically, we study the problem of a single impurity in a spin ladder by exact diagonalization to obtain the low-lying excitations. At finite concentrations and to leading order in the inter-rung coupling, we compare the spectra obtained from numerical diagonalization of large systems within the single-triplet subspace with the results of diagrammatic techniques, namely low-concentration and coherent-potential approximations. The contribution of small impurity clusters to the density of states is also discussed.Compartir:
Magnetismo cuántico en sistemas de baja dimensionalidad Autores:Arlego, Marcelo José Fabián Fecha: 2004-01-01Tipo de documento: Tesis de doctoradoResumen:Los objetivos de esta tesis consisten en analizar en una primera etapa la estructura de plateaux en curvas de magnetización y diagramas de fase magnéticos en sistemas de magnetismo cuántico unidimensionales. Desde el punto de vista de teorías efectivas, esto consiste en analizar el efecto de ciertas perturbaciones, tales como cuasiperiodicidad, desorden y anisotropías sobre modelos críticos, en particular líquidos de Luttinger. Para ello se han empleado técnicas provenientes de la teoría de campos, tales como bosonización (excepto para tratar el desorden), grupo de renormalización y algunos resultados de teorías de campos cuánticos conformes. También se utilizan técnicas numéricas sobre los modelos discretos las cuales dan soporte, complementan y verifican la validez de las predicciones de los modelos efectivos. En la segunda parte de la tesis se ha estudiado el efecto de impurezas en escaleras de espín de dos patas utilizando herramientas estándar de materia condensada tales como los métodos diagramáticos y métodos de funciones de Green, complementados con técnicas numéricas. La motivación para el uso de estas técnicas se basa en el hecho de que son adecuadas para ciertos regímenes perturbativos en los que nos hemos concentrado y permiten el modelado de situaciones más realistas donde se incorpora desorden a través del agregado de impurezas, que por otro lado son inevitables en cualquier sistema real.Compartir:
Competing interactions in the XYZ model Autores:Arlego, Marcelo José Fabián Cabra, Daniel Carlos Drut, Joaquín Emiliano Grynberg, Marcelo Daniel Fecha: 2003-04-01Tipo de documento: ArticuloResumen:We study the interplay between an XY anisotropy γ, exchange modulations, and an external magnetic field along the z direction in an XYZ chain using bosonization and Lanczos diagonalization techniques. We find an Ising critical line in the space of couplings which occur due to competing relevant perturbations that are present. More general situations are also discussed.Compartir:
Interplay between quasiperiodicity and disorder in quantum spin chains in a magnetic field Autores:Arlego, Marcelo José Fabián Fecha: 2002-08-29Tipo de documento: PreprintResumen:We study the interplay between disorder and a quasiperiodic coupling array in an external magnetic field in a spin-1/2 XXZ chain. A simple real space decimation argument is used to estimate the magnetization values where plateaux show up. The latter are in good agreement with exact diagonalization results on fairly long XX chains. Spontaneous susceptibility properties are also studied, finding a logarithmic behavior similar to the homogeneously disordered case.Compartir:
Quasiperiodic spin chains in a magnetic field Fecha: 2001-09-12Tipo de documento: ArticuloResumen:We study the interplay between a (quasi) periodic coupling array and an external magnetic field in a spin-1/2 XXZ chain. A new class of magnetization plateau is obtained by means of Abelian bosonization methods which gives rise to a sufficient quantization condition. The investigation of magnetic phase diagrams via exact diagonalization of finite clusters finds a complete agreement with the continuum treatment in a variety of situations.Compartir:
