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In this paper, to characterize the effect of topological defects on the entanglement of topological states, we introduce the concept of local entanglement entropy. By using the spinless p x + i p y superconductor with quantized vortices, we numerically calculated the local entanglement entropy. In the topological superconducting (weak-pairing) phase, we found that the local entanglement entropy turns to 0.5 for a Majorana zero mode. For the system with two/four Majorana zero modes, by calculating local entanglement entropy, we found the non-locality effect of Majorana zero modes. In the future, we will use local entanglement entropy to characterize the defect effect on other many-body systems with long entanglement, for example, topological order and quantum spin liquid. [ABSTRACT FROM AUTHOR]

In this paper, we numerically study the non-Abelian statistics of the zero-energy Majorana fermions at the end of Majorana chain and show its application to quantum computing by mapping it to a spin model with special symmetry. In particular, by using transverse-field Ising model with Z2 symmetry, we verify the nontrivial non-Abelian statistics of Majorana fermions. Numerical evidence and comparison in both Majorana representation and spin representation are presented. The degenerate ground states of a symmetry protected spin chain therefore provide a promising platform for topological quantum computation. [ABSTRACT FROM AUTHOR]

Recently, Majorana fermions (MFs) have attracted intensive attention due to their exotic statistics and possible applications in topological quantum computation. They are proposed to exist in various two-dimensional (2D) topological systems, such as topological superconductor (SC) and nanowire-superconducting hybridization system. In this paper, we point out that Majorana fermions in different topological systems obey different types of polygon sign rules. A numerical approach is described to identify the type of polygon sign rule of the Majorana fermions. Applying the approach to study two 2D topological systems, we find that vortex-induced Majorana fermions obey topological polygon sign rule and line-defect-induced Majorana fermions obey normal polygon sign rule. [ABSTRACT FROM AUTHOR]

A field experiment was conducted to study the effects of planting pattern (ridge culture, flatten culture, furrow culture) and film mulching on the distribution of spring maize root system and their influence on the yield of spring maize in the hilly area of central Sichuan basin. The results showed that ridge and film mulching had great influence on root morphology and root distribution of maize. The root length, root surface area and root volume of film mulching was 42.3%, 50.0%, 57.4% higher than those of no film mulching at jointing stage. The film mulching significantly increased the dry mass of root in vertical and horizontal distribution, and increased the root allocation ratio in deeper soil layer (20-40 cm) and the allocation ratio of wide row (0-20 cm) in horizontal direction. The effects of planting pattern on root growth and root distribution differed by film mulching. With film mulching, the ridge culture significantly increased the root dry mass in each soil layer and enlarged the distribution percentage of wide row (20-40 cm) in horizontal direction, as well as the dry mass of root in horizontal distribution and the root allocation ratio of wide row. The root mass under film mulching was in the order of ridge culture>flatten culture>furrow culture. Without film mulching, the furrow culture significantly increased root dry mass of narrow row (0-40 cm), and the root mass under no film mulching was in the order of furrow culture > ridge culture >flatten culture. As for the spike characteristics and maize yield, the filming mulching mea-sures reduced the corn bald length while increased the spike length, grain number, 1000-grain mass and yield. The yield under film mulching was in the order of ridge culture>flatten culture> furrow culture, while it was furrow culture > flatten culture > ridge culture under no film mulching. The reason for yield increase under ridge culture with film mulching was that it increased root weight especially in deep soil, and promoted the root allocation ratio in deeper soil and wide row (20-40 cm) in horizontal direction. The ridge-furrow culture without film mulching was helpful to root growth and increased the maize yield.