International Journal of Modern Physics B

This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. The subject is presented in a self-contained and pedagogical way. The VBS state was first introduced in the celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki (abbreviation AKLT is widely used). It became essential in condensed matter physics and quantum information (measurement-based quantum computation). Many publications have been devoted to the subject. Recently entanglement was studied in the VBS state. In this review, we start with the definition of a general AKLT spin chain and the construction of VBS ground state. In order to study entanglement, a block subsystem is introduced and described by the density matrix. Density matrices of 1-dimensional models are diagonalized and the entanglement entropies (the von Neumann entropy and Rényi entropy) are calculated. In the large block limit, the entropies also approach finite limits. Study of the spectrum of the density matrix led to the discovery that the density matrix is proportional to a projector.

We calculated the isomer spectrum of C₃₀ cluster by time-going-backward quasi-dynamics method and performed molecular dynamic simulations of the cluster growth in He buffer gas at 2500 K. Based on geometrical shapes, the isomers can be classified into closed cages, open cages, bowls, sheets and other irregular shapes. Although potential energies and free energies of the sheet isomers are much higher than those of the closed cage isomers, the dynamical simulations show that the sheet isomers rather than the cage isomers dominate in the resultant clusters at the simulation temperature and the most probable sheet isomer lies on the 47th level counted from the bottom one of the isomer spectrum.

SKS active carbon, prepared by dehydrogenation of the polystyrene–divinylbenzene copolymer, as a model sample of highly amorphous carbons, has been examined by scanning electron microscopy, transmission electron microscopy, and energy dispersive X-ray methods, indicating a nanostructural nonperiodic character of the resulting product. No crystalline-like particles are experimentally found in the bulk. The PSDVB copolymer dehydrogenation has been quantum chemically (QC) simulated to describe the interconnecting amorphous phase. A set of clusters with a different degree of carbonization has been QC evaluated. The first level model of the amorphous active carbon has been proposed.

The water wave transmission properties and the frequency spectra of one-dimensional combination bottom of water and mercury with different filling fractions are studied by the transfer matrix method. For the periodic bottoms (PBs), the effect of the steps' numbers and the width on the band gaps are discussed. Each of whole band gaps is the juxtaposition of the gaps of three kinds of PBs, without covering. The numerical results show that the band gaps could be enlarged effectively by choosing the steps' width properly.

SrO-borovanadate glasses with the nominal composition (V₂O₅)_z(SrO)_0.2( B₂O₃)_0.8-z, 0.4≤z ≤0.8 were studied by direct current (DC) electrical conductivity, inductively coupled plasma (ICP) spectroscopy, Fourier transform infrared (FT-IR) spectroscopy and X-ray-powder-diffraction (XRD). These glasses were prepared by a normal quench technique and the actual compositions of the glasses were determined by ICP spectroscopy. XRD patterns confirm the amorphous nature of the present glasses. The temperature dependence of DC electrical conductivity of these glasses has been studied in terms of different hopping models. The IR results agree with previous investigations on similar glasses and it has been concluded that similar to SrO-vanadate glasses, metavandate chainlike structures of SrV₂O₆ and individual VO₄ units also occur in these SrO-borovanadate glasses. The SrV₂O₆ and VO_n polyhedra predominate in the low B₂O₃ containing SrO-borovanadate glasses as the B substitutes into the V sites of the various VO_n polyhedra and only when the B₂O₃ concentration exceeds the SrO content do BO_n structures appear. This qualitative picture of three distinct structural groupings for the Sr-vanadate and Sr-borovanadate glasses is consistent with the proposed glass structure on previous IR and extended X-ray absorption fine structure (EXAFS) studies on these types of glasses. The conductivity results were analyzed with reference to theoretical models existing in the literature and the analysis shows that the conductivity data are consistent with Mott's nearest neighbor hopping model. However, both Mott VRH and Greaves models are suitable to explain the data. Schnakenberg's generalized polaron hopping model is also consistent with the temperature dependence of the activation energy, but the various model parameters such as density of states, hopping energy obtained from the best fits were found to be not in accordance with the prediction of the Mott model.

In multi-agent system (MAS), the communication topology of agent network plays a very important role in its collaboration. Small-world networks are the networks with high local clustering and small average path length, and the communication networks of MAS can be analyzed within the frame of small-world topology. Yet the real multiagent communication networks are abundant and the classical WS small-world model is not suitable for all cases. In this paper, two new small-world network models are presented. One is based on random graph substrate and local nodes preference reconnection and the other is based on regular graph substrate and long-range nodes preference reconnection. The characteristic of the network parameter such as the clustering coefficients, average path length, and eigenvalue λ₂ and λ_n of the Laplacian matrix for these two models and WS model is studied. The consensus problem that based on these three models is also studied. An example is given and the conclusions are made in the end.