750 research outputs found
Model wavefunctions for interfaces between lattice Laughlin states
We study the interfaces between lattice Laughlin states at different
fillings. We propose a class of model wavefunctions for such systems
constructed using conformal field theory. We find a nontrivial form of charge
conservation at the interface, similar to the one encountered in the field
theory works from the literature. Using Monte Carlo methods, we evaluate the
correlation function and entanglement entropy at the border. Furthermore, we
construct the wavefunction for quasihole excitations and evaluate their mutual
statistics with respect to quasiholes originating at the same or the other side
of the interface. We show that some of these excitations lose their anyonic
statistics when crossing the interface, which can be interpreted as
impermeability of the interface to these anyons. Contrary to most of the
previous works on interfaces between topological orders, our approach is
microscopic, allowing for a direct simulation of e.g. an anyon crossing the
interface. Even though we determine the properties of the wavefunction
numerically, the closed-form expressions allow us to study systems too large to
be simulated by exact diagonalization.Comment: A number of changes were made in response to referees' comments:
large parts of the text were rewritten, new results were added, some of the
old results were reinterpreted, the discussion of connection to earlier works
was expande
Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in flat bands
We perform an exact-diagonalization study of quasihole excitations for the
two-component Halperin state in the lowest Landau level and for several
bosonic fractional Chern insulators in topological flat bands with
Chern number . Properties including the quasihole size, charge, and
braiding statistics are evaluated. For the Halperin model state, we
observe isotropic quasiholes with a clear internal structure, and obtain the
quasihole charge and statistics matching the theoretical values. Interestingly,
we also extract the same quasihole size, charge, and braiding statistics for
the continuum model states of fractional Chern insulators, although the
latter possess a "color-entangled" nature that does not exist in ordinary
two-component Halperin states. We also consider two real lattice models with a
band having . There, we find that a quasihole can exhibit much stronger
oscillations of the density profile, while having the same charge and
statistics as those in the continuum models.Comment: 11 pages, 10 figures, small changes in the text related to the review
process (mostly improved presentation of the color-entangled BC), added
bibliographical detail
Analysis of the Stage
The primary objective of this paper is to design a method of detecting
road edges without using complex algorithms to identify and analyze
images. Instead, neural networks are used, which allows to enhance and facilitate this process. The paper describes a program that recognizes the road in a picture with the use of a neural network trained on 500 samples. The samples contain original photos and images with a selected road. In the course of the research two solutions arose. The first solution is to use a single Perceptron to recognize the road. The second solution is to classify the photos using a Kohonen network and establish a separate network for each class
The relationship of organizational health and school safety to student achievement
Educators are compelled by federal and state legislation to investigate multiple aspects of the school organization to address factors that may increase student achievement. This study addressed this issue by investigating organizational health and school safety in urban elementary schools and their relationships to student achievement. The study explored elementary school teachers\u27 perceptions regarding organizational health and school safety. These data were correlated to student achievement on the Virginia Standards of Learning Tests in English and mathematics for fifth grade.;The Organizational Health Inventory (OHI) for elementary schools was used to survey teachers\u27 perceptions of institutional integrity, collegial leadership, resource influence, teacher affiliation, and academic emphasis in 24 urban elementary schools in Virginia. The School Safety Survey (SSS) gathered data on teachers\u27 perceptions of school safety. The fifth grade Virginia Standards of Learning (SOL) tests in the areas of English and mathematics were the measurement tools for student achievement. This study compared the overall health indices and the subscale scores of organizational health to school safety, achievement in English, and achievement in mathematics. It further investigated the relationship between school safety and achievement in English as well as achievement in mathematics.;The study showed that there was a strong positive relationship between organizational health and safety, organizational health and student achievement in both English and mathematics, and school safety and student achievement in both English and mathematics. Regression analysis of the subscales of organizational health revealed that academic emphasis had a strong independent effect on student achievement in English and mathematics. Correlation and regression analysis with regard to organizational health and safety indicated that organizational health had an independent effect on English, but not mathematics
Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
We use conformal field theory to construct model wavefunctions for an
interface between lattice versions of a bosonic Laughlin state and a
fermionic Moore-Read state. The properties of the resulting model
state, such as particle density, correlation function and R\'enyi entanglement
entropy are then studied using the Monte Carlo approach. Moreover, we construct
the wavefunctions also for localized anyonic excitations (quasiparticles and
quasiholes). We study their density profile, charge and statistics. We show
that, similarly to the Laughlin-Laughlin case studied earlier, some anyons (the
Laughlin Abelian ones) can cross the interface, while others (the non-Abelian
ones) lose their anyonic character in such a process. Also, we argue that,
under an assumption of local particle exchange, multiple interfaces give rise
to a topological degeneracy, which can be interpreted as originating from
Majorana zero modes.Comment: 17 pages, 14 figure
Theater auf der Wieden - History of location, audiences, and mechanics
There are many historical connections between Vienna’s theater scene and the original theater that Mozart’s Die Zauberflöte was performed in. This paper discusses the audiences of the Theater, the location, architecture and mechanics. Although much has changed within theaters since the 18th century, some things still remain the same
Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands
We investigate an interaction-driven transition between crystalline and liquid states of strongly correlated spinless fermions within topological flat bands at low density (with filling factors nu = 1/5, 1/7, 1/9). Using exact diagonalization for finite-size systems with periodic boundary conditions, we distinguish different phases, whose stability depends on the interaction range, controlled by the screening parameter of the Coulomb interaction. The crystalline phases are identified by a crystallization strength, calculated from the Fourier transforms of pair correlation density, while the fractional Chern insulator (FCI) phases are characterized using momentum counting rules, entanglement spectrum, and overlaps with corresponding fractional quantum Hall states. The type of the phase depends on a particular single-particle model and its topological properties. We show that for nu = 1/7 and 1/5 it is possible to tune between theWigner crystal and fractional Chern insulator phase in the kagome lattice model with the band carrying the Chern number C = 1. In contrast, in the C = 2 models, the Wigner crystallization was absent at nu = 1/5, and appeared at nu = 1/9, suggesting that C = 2 FCIs are more stable agains
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