Quantum Entanglement of Non-Hermitian Quasicrystals

As a hallmark of pure quantum effect, quantum entanglement has provided unconventional routes to condensed matter systems. Here, from the perspective of quantum entanglement, we disclose exotic quantum physics in non-Hermitian quasicrystals. We present a class of experimentally realizable models for non-Hermitian quasicrystal chains, in which asymmetric hopping and complex potential coexist. We diagnose global phase diagram by means of entanglement from both real-space and momentum-space partition. By measuring entanglement entropy, we numerically determine the metal-insulator transition point. We combine real-space and momentum-space entanglement spectra to complementarily characterize the delocalization phase and the localization phase. Inspired by entanglement spectrum, we further analytically prove that a duality exists between the two phase regions. The transition point is self-dual and exact, further validating the numerical result from diagonalizing non-Hermitian matrices. Finally, we identify mobility edge by means of entanglement

Summary of the Chinese chive transcriptome sequencing using the Illumina HiSeq.

<p>Summary of the Chinese chive transcriptome sequencing using the Illumina HiSeq.</p

<i>De Novo</i> Assembly and Annotation of the Chinese Chive (<i>Allium tuberosum</i> Rottler ex Spr.) Transcriptome Using the Illumina Platform

<div><p>Chinese chive (<i>A</i>. <i>tuberosum</i> Rottler ex Spr.) is one of the most widely cultivated <i>Allium</i> species in China. However, minimal transcriptomic and genomic data are available to reveal its evolution and genetic diversity. In this study, de novo transcriptome sequencing was performed to produce large transcript sequences using an Illumina HiSeq 2000 instrument. We produced 51,968,882 high-quality clean reads and assembled them into 150,154 contigs. A total of 60,031 unigenes with an average length of 631 bp were identified. Of these, 36,523 unigenes were homologous to existing database sequences, 35,648 unigenes were annotated in the NCBI non-redundant (Nr) sequence database, and 23,509 unigenes were annotated in the Swiss-Prot database. A total of 26,798 unigenes were assigned to 57 Gene Ontology (GO) terms, and 13,378 unigenes were assigned to Cluster of Orthologous Group categories. Using the Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway database, we mapped 21,361 unigenes onto 128 pathways. Furthermore, 2,125 sequences containing simple sequence repeats (SSRs) were identified. This new dataset provides the most comprehensive resource currently available for gene expression, gene discovery, and future genomic research on Chinese chive. The sequence resources developed in this study can be used to develop molecular markers that will facilitate further genetic research on Chinese chive and related species.</p></div

Unigene homology searches against the NR database.

<p>(A) The E-value distribution of BLAST hits for the assembled unigenes in the NR database. (B) The similarity distribution of BLAST hits against the NR database for each unigene. (C) Species distribution of the top BLASTx hits against the NR database for each unigene.</p

Overview of the transcriptome assembly for <i>A</i>. <i>tuberosum</i> Rottler ex Spr.

<p>(A) Size distribution of contigs; (B) size distribution of unigenes.</p

Summary of the Chinese chive transcriptome sequencing using the Illumina HiSeq.

<p>Summary of the Chinese chive transcriptome sequencing using the Illumina HiSeq.</p

GO classification of assembled sequences.

<p>A total of 13,897 unigenes were grouped into three main GO categories: ‘Biological Processes’, ‘Cellular Component’, and ‘Molecular Function’.</p

Frequency of dinucleotide and trinucleotide SSRs repeat motifs in <i>A</i>. <i>tuberosum</i>.

<p>Frequency of dinucleotide and trinucleotide SSRs repeat motifs in <i>A</i>. <i>tuberosum</i>.</p

Statistical summary of the de novo transcriptome assembly for <i>A</i>. <i>tuberosum</i> Rottler ex Spr.

<p>Statistical summary of the de novo transcriptome assembly for <i>A</i>. <i>tuberosum</i> Rottler ex Spr.</p

Statistics of the SSRs identified in the <i>A</i>. <i>tuberosum</i> transcriptome.

<p>Statistics of the SSRs identified in the <i>A</i>. <i>tuberosum</i> transcriptome.</p