Criticality in Translation-Invariant Parafermion Chains

In this work we numerically study critical phases in translation-invariant $\mathbb{Z}_N$ parafermion chains with both nearest- and next-nearest-neighbor hopping terms. The model can be mapped to a $\mathbb{Z}_N$ spin model with nearest-neighbor couplings via a generalized Jordan-Wigner transformation and translation invariance ensures that the spin model is always self-dual. We first study the low-energy spectrum of chains with only nearest-neighbor coupling, which are mapped onto standard self-dual $\mathbb{Z}_N$ clock models. For $3\leq N\leq 6$ we match the numerical results to the known conformal field theory(CFT) identification. We then analyze in detail the phase diagram of a $N=3$ chain with both nearest and next-nearest neighbor hopping and six critical phases with central charges being $4/5$, 1 or 2 are found. We find continuous phase transitions between $c=1$ and $c=2$ phases, while the phase transition between $c=4/5$ and $c=1$ is conjectured to be of Kosterlitz-Thouless type.Comment: published versio

Topology and Criticality in Resonating Affleck-Kennedy-Lieb-Tasaki loop Spin Liquid States

We exploit a natural Projected Entangled-Pair State (PEPS) representation for the resonating Affleck-Kennedy-Lieb-Tasaki loop (RAL) state. By taking advantage of PEPS-based analytical and numerical methods, we characterize the RAL states on various two-dimensional lattices. On square and honeycomb lattices, these states are critical since the dimer-dimer correlations decay as a power law. On kagome lattice, the RAL state has exponentially decaying correlation functions, supporting the scenario of a gapped spin liquid. We provide further evidence that the RAL state on the kagome lattice is a $\mathbb{Z}_2$ spin liquid, by identifying the four topological sectors and computing the topological entropy. Furthermore, we construct a one-parameter family of PEPS states interpolating between the RAL state and a short-range Resonating Valence Bond state and find a critical point, consistent with the fact that the two states belong to two different phases. We also perform a variational study of the spin-1 kagome Heisenberg model using this one-parameter PEPS.Comment: 10 pages, 14 figures, published versio

Investigating operations of industrial parks in Beijing: efficiency at different stages

Industrial parks enjoy significant importance in many countries and regions. This study presents a multi-stage operational process to evaluate the efficiency of parks at each stage using an empirical study of Beijing. The study finds that only three of 22 parks were efficient overall during 2006–2008 and two of 22 were efficient during 2009–2012. The promotion of business, facilitation of production, and rewards of economic returns are highly correlated stages for efficiency performance. The results suggest that Beijing’s government should expend more effort developing the potential to generate outputs given current land and investment inputs. In addition, it provides a tool to strengthen the organisational capacity development of industrial parks by emphasising their multi-dimensions in inputs and outputs, selecting the right competitors at the right organisational stage, locating sources of efficiency and inefficiency, and understanding progression and balance of internal stages during operation

Identifiability of Label Noise Transition Matrix

The noise transition matrix plays a central role in the problem of learning with noisy labels. Among many other reasons, a large number of existing solutions rely on access to it. Identifying and estimating the transition matrix without ground truth labels is a critical and challenging task. When label noise transition depends on each instance, the problem of identifying the instance-dependent noise transition matrix becomes substantially more challenging. Despite recent works proposing solutions for learning from instance-dependent noisy labels, the field lacks a unified understanding of when such a problem remains identifiable. The goal of this paper is to characterize the identifiability of the label noise transition matrix. Building on Kruskal's identifiability results, we are able to show the necessity of multiple noisy labels in identifying the noise transition matrix for the generic case at the instance level. We further instantiate the results to explain the successes of the state-of-the-art solutions and how additional assumptions alleviated the requirement of multiple noisy labels. Our result also reveals that disentangled features are helpful in the above identification task and we provide empirical evidence.Comment: Preprint. Under review. For questions please contact [email protected]

Commercial Janus Fabrics as Reusable Facemask Materials: A Balance of Water Repellency, Filtration Efficiency, Breathability, and Reusability

Facemasks as personal protective equipment play a significant role in helping prevent the spread of viruses during the COVID-19 pandemic. A desired reusable fabric facemask should strike a balance of water repellency, good filtration efficiency (FE), breathability, and mechanical robustness against washing cycles. Despite significant efforts in testing various commercial fabric materials for filtration efficiency, few have investigated fabric performance as a function of the fiber/yarn morphology and wettability of the fabric itself. In this study, we examine commercial fabrics with Janus-like behaviors to determine the best reusable fabric facemask materials by understanding the roles of morphology, porosity, and wettability of the fabric on its overall performance. We find that the outer layer of the diaper fabric consisted of laminated polyurethane, which is hydrophobic, has low porosity (∼5%) and tightly woven yarn structures, and shows the highest overall FE (up to 54%) in the submicron particle size range (0.03-0.6 μm) among the fabrics tested. Fabric layers with higher porosity lead to lower-pressure drops, indicating higher breathability but lower FE. Tightly woven waterproof rainwear fabrics perform the best after 10 washing cycles, remaining intact morphologically with only a 2-5% drop in the overall FE in the submicron particle size range, whereas other knitted fabric layers become loosened and the laminated polyurethane thin film on the diaper fabric is wrinkled. In comparison, the surgical masks and N95 respirators made from nonwoven polypropylene (PP) fibers see over a 30% decline in the overall FE after 10 washing cycles. Overall, we find that tightly woven Janus fabrics consisting of a low porosity, a hydrophobic outer layer, and a high porosity and hydrophilic inner layer offer the best performance among the fabrics tested as they can generate a high overall FE, achieve good breathability, and maintain fabric morphology and performance over multiple washing cycles

Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems

The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of conceptual importance, but also provide great opportunities towards experimental realization since space group symmetries naturally exist for any realistic material. In this paper, we systematically classify the crystalline topological superconductors (TSC) and topological insulators (TI) in 2D interacting fermionic systems by using an explicit real-space construction. In particular, we discover an intriguing fermionic crystalline topological superconductor that can only be realized in interacting fermionic systems (i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for generic 2D interacting fermionic systems.Comment: 39+37 pages, 10+13 figures, 3+1 tables, all comments and suggestions are very welcom