Composite Boson Mapping for Lattice Boson Systems

We present a canonical mapping transforming physical boson operators into quadratic products of cluster composite bosons that preserves matrix elements of operators when a physical constraint is enforced. We map the 2D lattice Bose-Hubbard Hamiltonian into $2\times 2$ composite bosons and solve it at mean field. The resulting Mott insulator-superfluid phase diagram reproduces well Quantum Monte Carlo results. The Higgs boson behavior along the particle-hole symmetry line is unraveled and in remarkable agreement with experiment. Results for the properties of the ground and excited states are competitive with other state-of-the-art approaches, but at a fraction of their computational cost. The composite boson mapping here introduced can be readily applied to frustrated many-body systems where most methodologies face significant hurdles.Comment: 8 pages, 4 figure

Staircase of crystal phases of hard-core bosons on the Kagome lattice

We study the quantum phase diagram of a system of hard-core bosons on the Kagome lattice with nearest-neighbor repulsive interactions, for arbitrary densities, by means of the hierarchical mean field theory and exact diagonalization techniques. This system is isomorphic to the spin S=1/2 XXZ model in presence of an external magnetic field, a paradigmatic example of frustrated quantum magnetism. In the non-frustrated regime, we find two crystal phases at densities 1/3 and 2/3 that melt into a superfluid phase when increasing the hopping amplitude, in semi-quantitative agreement with quantum Monte Carlo computations. In the frustrated regime and away from half-filling, we find a series of plateaux with densities commensurate with powers of 1/3. The broader density plateaux (at densities 1/3 and 2/3) are remnants of the classical degeneracy in the Ising limit. For densities near half-filling, this staircase of crystal phases melts into a superfluid, which displays finite chiral currents when computed with clusters having an odd number of sites. Both the staircase of crystal phases and the superfluid phase prevail in the non-interacting limit, suggesting that the lowest dispersionless single-particle band may be at the root of this phenomenon

Chiral phases of two-dimensional hard-core bosons with frustrated ring-exchange

We study the zero temperature phase diagram of two-dimensional hard-core bosons on a square lattice with nearest neighbour and plaquette (ring-exchange) hoppings, at arbitrary densities, by means of a hierarchical mean-field theory. In the frustrated regime, where quantum Monte Carlo suffers from a sign problem, we find a rich phase diagram where exotic states with nonzero chirality emerge. Among them, novel insulating phases, characterized by nonzero bond-chirality and plaquette order, are found over a large region of the parameter space. In the unfrustrated regime, the hierarchical mean-field approach improves over the standard mean-field treatment as it is able to capture the transition from a superfluid to a valence bond state upon increasing the strength of the ring-exchange term, in qualitative agreement with quantum Monte Carlo results

Density-dependent synthetic magnetism for ultracold atoms in optical lattices

Raman-assisted hopping can allow for the creation of density-dependent synthetic magnetism for cold neutral gases in optical lattices. We show that the density-dependent fields lead to a non-trivial interplay between density modulations and chirality. This interplay results in a rich physics for atoms in two-leg ladders, characterized by a density-driven Meissner- to vortex-superfluid transition, and a non-trivial dependence of the density imbalance between the legs. Density-dependent fields also lead to intriguing physics in square lattices. In particular, it leads to a density-driven transition between a non-chiral and a chiral superfluid, both characterized by non-trivial charge density-wave amplitude. We finally show how the physics due to the density-dependent fields may be easily probed in experiments by monitoring the expansion of doublons and holes in a Mott insulator, which presents a remarkable dependence on quantum fluctuations.Comment: 5 pages, 4 figure

Variational Quantum Simulation of Valence-Bond Solids

We introduce a hybrid quantum-classical variational algorithm to simulate ground-state phase diagrams of frustrated quantum spin models in the thermodynamic limit. The method is based on a cluster-Gutzwiller ansatz where the wave function of the cluster is provided by a parameterized quantum circuit whose key ingredient is a two-qubit real XY gate allowing to efficiently generate valence-bonds on nearest-neighbor qubits. Additional tunable single-qubit Z- and two-qubit ZZ-rotation gates allow the description of magnetically ordered and paramagnetic phases while restricting the variational optimization to the U(1) subspace. We benchmark the method against the $J1-J2$ Heisenberg model on the square lattice and uncover its phase diagram, which hosts long-range ordered Neel and columnar anti-ferromagnetic phases, as well as an intermediate valence-bond solid phase characterized by a periodic pattern of 2×2 strongly-correlated plaquettes. Our results show that the convergence of the algorithm is guided by the onset of long-range order, opening a promising route to synthetically realize frustrated quantum magnets and their quantum phase transition to paramagnetic valence-bond solids with currently developed superconducting circuit devices

Composite particle mean field theory for strongly correlated systems

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica de la Materia Condensada. Fecha de lectura: 30-10-2014Presentamos un método aplicable a Hamiltonianos que modelizan sistemas bosónicos y fermiónicos fuertemente correlacionados relevantes en física de la materia condensada y de átomos fríos en redes ópticas. El método propuesto resulta particularmente conveniente para describir aislantes de Mott y fases con correlaciones de corto alcance que emergen en sistemas frustrados bosónicos y de espín cuya descripción plantea serias dificultades a otros métodos del estado-del-arte. La idea fundamental reside en la identificación de conjuntos de grados de libertad de la red original (clusters) como las piezas básicas que capturan los rasgos esenciales de las fases presentes en el sistema objeto de estudio. Presentamos los mappings canónicos que relacionan los operadores the espín, bosónicos y fermiónicos del modelo original con formas bilineales de unos nuevos operadores bosónicos y fermiónicos compuestos que representan los estados cuánticos de dichos clusters. Gracias a que el mapping es canónico, el Hamiltoniano de estudio puede reescribirse en términos de estos nuevos operadores compuestos y aproximarse mediante técnicas usuales de muchos cuerpos, con la ventaja de que las correlaciones cuánticas dentro de los clusters están incluidas de manera exacta por definición. Presentamos diferentes esquemas de campo medio autoconsistente aplicables a Hamiltonianos generales de partículas compuestas y con ellos estudiamos diferentes modelos. Concretamente, estudiamos un modelo de espines con interacción en anillo (ring exchange), hacemos benchmark de los modelos de Hubbard bosónico y fermiónico y estudiamos un sistema de bosones fuertemente correlacionados en presencia de un campo gauge artificial de flujo π. La teoría de partículas compuestas presentada en esta tesis permite obtener el diagrama de fases del estado fundamental de dichos modelos. El uso de clusters como grado de libertad permite la descripción de diferentes fases caracterizadas por diferentes órdenes de largo alcance. El esquema algebraico establecido mediante los mappings permite la computación de las excitaciones de baja energía como magnones en ferromagnetos o el modo de Higgs y de Goldstone en superfluidos. Además, permite diferentes extensiones y aproximaciones que puedan describir, por ejemplo, fases con correlaciones de largo alcance, o el estudio de dinámica de quenches en sistemas de átomos fríos.We present a simple method applicable to lattice spin, bosonic, and fermionic model Hamiltonians relevant for strongly correlated condensed matter and cold atom physics. In particular, it is well suited to describe short-range correlated phases emerging in frustrated spin and bosonic systems that pose significant problems to other state-of-the-art techniques. The key idea resides on the identification of clusters of the original degrees of freedom as the building blocks capturing the necessary quantum correlations to describe the essential features of the phases present in the system under study. We present the canonical mappings that relate the spin, bosonic and fermionic operators of the original lattice to bilinear forms of new composite bosons and fermions that describe the quantum many-body states of these clusters. The model of interest can be reexpressed in terms of this new set of composite operators and approached by standard manybody techniques, with the advantage that quantum correlations inside the cluster are automatically computed from the onset. We present various self-consistent mean-field schemes applicable to general composite particle Hamiltonians and apply them to diferent models. In particular, we study a model of spins with ring-exchange interaction, we benchmark the bosonic and fermionic Hubbard models, and study a system of strongly interacting bosons in the presence of a fux artificial gauge field. The composite particle mean field theory presented in this thesis allows to map the ground-state phase diagram of these models. The use of clusters as the basic degree of freedom allows for the description of diferent phases characterized by coexistence and competition of diferent orders. Finally, the algebraic framework set by the mappings allows for the computation of low-lying excitations such as magnon dispersions on ferromagnets or the Higgs and Goldstone modes in superfluids. Further extensions and approximation schemes may permit the description of long-range correlated phases, or the study of quench-dynamics in cold atom systems

Density-dependent synthetic magnetism for ultracold atoms in optical lattices

10 pags.; 6 figs.; PACS number(s): 67.85.−d, 03.65.Vf, 03.75.Lm© 2015 American Physical Society. Raman-assisted hopping can allow for the creation of density-dependent synthetic magnetism for cold neutral gases in optical lattices. We show that the density-dependent fields lead to a nontrivial interplay between density modulations and chirality. This interplay results in a rich physics for atoms in two-leg ladders, characterized by a density-driven Meissner-superfluid to vortex-superfluid transition, and a nontrivial dependence of the density imbalance between the legs. Density-dependent fields also lead to intriguing physics in square lattices. In particular, it leads to a density-driven transition between a nonchiral and a chiral superfluid, both characterized by nontrivial charge density-wave amplitude. We finally show how the physics due to the density-dependent fields may be easily probed in experiments by monitoring the expansion of doublons and holes in a Mott insulator, which presents a remarkable dependence on quantum fluctuations.We acknowledge support by the cluster of excellence QUEST, the DFG Research Training Group 1729, the SUTD start-up grant (Grant No. SRG-EPD-2012-045), and the Spanish Ministry of Economy and Competitiveness through Grants No. FIS-2012- 34479, No. BES-2010-031607, and No. EEBB-14-09077.Peer Reviewe

Composite fermion-boson mapping for fermionic lattice models

We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is satisfied. This condition is treated on average in a composite particle mean-field approach, which consists of an ansatz that decouples the composite fermionic and bosonic sectors. The theory is tested on the one- and two-dimensional Hubbard models. Using a Bogoliubov determinant for the composite fermions and either a coherent or Bogoliubov state for the bosons, we obtain a simple and accurate procedure for treating the Mott insulating phase of the Hubbard model with mean-field computational cost

Generación de biogás. Experiencia del tambo La Natividad, Coronel Dorrego, Buenos Aires

Este documento sintetiza un año de trabajo entre diferentes áreas del INTA, motivado por la agenda de problemas de productores de la región pampeana. El relato está centrado en la experiencia de “La Natividad” Tambo Fábrica de Coronel Dorrego, provincia de Buenos Aires. No obstante, ha sido interpelado por más de una veintena de casos que han demandado al Proyecto de Energía Renovable de INTA1 resolver problemas de efluentes/generación de biogás (energía). Nos proponemos describir el procedimiento de trabajo desarrollado con el objetivo de generar condiciones para que la experiencia se expanda a otras regiones y, como Institución, facilitemos procesos de aprendizaje. Hemos decidido contar el caso y relacionarlo con conceptos teóricos que fueron necesarios para explicar qué pasaba y fundamentar qué decisiones se tomaron.EEA OliverosFil: Huerga, Ignacio Roberto. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Oliveros; ArgentinaFil: Butti, Mariano. Instituto Nacional de Tecnología Agropecuaria (INTA). Instituto de Ingeniería Rural; ArgentinaFil: Intaschi, Daniel Horacio. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Barrow; ArgentinaFil: Massigoge, Jose Ignacio. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Barrow; ArgentinaFil: Pusineri, Leandro Jose. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Barrow. Oficina De Información Técnica San Cayetano; ArgentinaFil: Justianovich, Sergio Hernan. Instituto Nacional de Tecnología Agropecuaria (INTA). Centro de Investigación y Desarrollo Tecnológico para la Agricultura Familiar. Instituto de Investigación y Desarrollo Tecnológico para la Agricultura Familiar Región Pampeana; Argentin

Enseñanza de matemáticas a distancia en grados en ingeniería y física

Las asignaturas de Matemáticas en grados de Física e Ingeniería tienen un carácter eminentemente instrumental, a pesar de ser a menudo asignaturas troncales. Por su contenido abstracto y el formalismo y rigor propios, resultan especialmente duras a los estudiantes que no dominan los conocimientos previos requeridos. A estas dificultades se añaden las propias de cursar estas asignaturas en una universidad a distancia: ausencia de un espacio físico común con profesores y compañeros y diversas obligaciones añadidas de los estudiantes. Todo esto se traduce en una baja motivación de los estudiantes al enfrentarse a ellas, resultados negativos e incluso abandono. Varios profesores de la UNED nos hemos constituido como grupo de innovación docente con el objetivo de utilizar los recursos disponibles para revertir esta situación. Uno de nuestros objetivos es fomentar el papel de la visualización en Matemáticas a través de la creación de materiales adaptados a los entornos virtuales y haciendo especial hincapié en las diversas aplicaciones a la Física o Ingeniería que ayudan a motivar, comprender y aprender las Matemáticas en estos grados. En este trabajo presentaremos las principales iniciativas que hemos llevado a cabo hasta ahora, los resultados obtenidos y algunas líneas en las que nos gustaría seguir trabajando