Truncation of lattice fractional quantum Hall Hamiltonians derived from conformal field theory

Conformal field theory has recently been applied to derive few-body Hamiltonians whose ground states are lattice versions of fractional quantum Hall states. The exact lattice models involve interactions over long distances, which is difficult to realize in experiments. It seems, however, that such long-range interactions should not be necessary, as the correlations decay exponentially in the bulk. This poses the question, whether the Hamiltonians can be truncated to contain only local interactions without changing the physics of the ground state. Previous studies have in a couple of cases with particularly much symmetry obtained such local Hamiltonians by keeping only a few local terms and numerically optimizing the coefficients. Here, we investigate a different strategy to construct truncated Hamiltonians, which does not rely on optimization, and which can be applied independent of the choice of lattice. We test the approach on two models with bosonic Laughlin-like ground states with filling factor $1/2$ and $1/4$, respectively. We first investigate how the coupling strengths in the exact Hamiltonians depend on distance, and then we study the truncated models. For the case of $1/2$ filling, we find that the truncated model with truncation radius $\sqrt{2}$ lattice constants on the square lattice and $1$ lattice constant on the triangular lattice has an approximate twofold ground state degeneracy on the torus, and the overlap per site between these states and the states constructed from conformal field theory is higher than $0.99$ for the lattices considered. For the model at $1/4$ filling, our results give some hints that a truncation radius of $\sqrt{5}$ on the square lattice and $\sqrt{7}$ on the triangular lattice might be enough, but the finite size effects are too large to judge whether the topology is, indeed, present in the thermodynamic limit.Comment: 8 Pages, 10 Figure

Post-Pandemic Sustainable Business Solution

Copyright © 2021 The Author(s). In this research, we examined some of the key concerns faced by businesses from various industries which are associated with the COVID-19 pandemic. To extend the existing research, we also evaluate perspectives on sustainable recovery solutions proposed by the business. This market research, supported by academic research, is intended to support businesses and the Government in tapering their approach to achieving sustainable economic recovery. A total of 16 different industries participated in our research project and the findings of our research provide an evidence-based perspective on how businesses are responding to the pandemic and planning for the post-COVID era. This evidence document outlines recommendations on potential support packages and areas of focus for the Government to consider, based on recent survey data, lessons learnt from the past, professional experience and respected academic models.This research received no external fundin

Ultraviolet Extinction Properties in the Milky Way

We have assembled a homogeneous database of 417 ultraviolet (UV) extinction curves for reddened sightlines having International Ultraviolet Explorer (IUE) spectra. We have combined these with optical and 2MASS photometry allowing estimates of the ratio of total-to-selective extinction, R(V), for the entire sample. Fitzpatrick-Massa (FM) parameters have also been found for the entire sample. This is the largest study of parameterized UV extinction curves yet published and it covers a wide range of environments, from dense molecular clouds to the diffuse interstellar medium (ISM), with extinctions A(V) ranging from 0.50 to 4.80. It is the first to extend far beyond the solar neighborhood and into the Galaxy at large, with 30 sightlines having distances > 5 kpc. Previously, the longest sightlines with FM parameters and R(V) extended ~ 1 kpc. We find that (1.) the CCM extinction law applies for 93% of the sightlines, implying that dust processing in the Galaxy is efficient and systematic; (2.) the central wavelength of the 2175 A bump is constant; (3.) the 2175 A bump width is dependent on environment. Only four sightlines show systematic deviations from CCM, HD 29647, 62542, 204827, and 210121. These sightlines all sample dense, molecule-rich clouds. The new extinction curves and values of R(V) allow us to revise the CCM law.Comment: 32 pages, 12 figure

Design space exploration for providing QoS within the HARMONY framework

ABSTRACT The HARMONY architectur