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 ∣C∣=2|C|=2 flat bands

We perform an exact-diagonalization study of quasihole excitations for the two-component Halperin $(221)$ state in the lowest Landau level and for several $\nu=1/3$ bosonic fractional Chern insulators in topological flat bands with Chern number $|C|=2$. Properties including the quasihole size, charge, and braiding statistics are evaluated. For the Halperin $(221)$ 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 $|C|=2$ 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 $|C|=2$. 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 $\nu=1/2$ Laughlin state and a fermionic $\nu=5/2$ 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