Entanglement in Valence-Bond-Solid States

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 Renyi 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.Comment: Published version, 80 pages, 8 figures; references update

A Test of Some Principles In Information Campaign Planning

ALTHOUGH INFORMATION campaigns are standard fare for agricultural colleges and the U. S. Department of Agriculture, the campaign reported here may be of special interest for at least three reasons

Efforts to Increase Pesticide Label-Reading

Four years of work with the Pesticides Regulation Division of the U. S. Environmental Protection Agency have given us a unique opportunity to learn something about pesticide labels and the dynamics of their use

Popular attitudes to memory, the body, and social identity : the rise of external commemoration in Britain, Ireland, and New England

A comparative analysis of samples of external memorials from burial grounds in Britain, Ireland and New England reveals a widespread pattern of change in monument style and content, and exponential growth in the number of permanent memorials from the 18th century onwards. Although manifested in regionally distinctive styles on which most academic attention has so far been directed, the expansion reflects global changes in social relationships and concepts of memory and the body. An archaeological perspective reveals the importance of external memorials in articulating these changing attitudes in a world of increasing material consumption

Genome-wide association scan meta-analysis identifies three Loci influencing adiposity and fat distribution.

To identify genetic loci influencing central obesity and fat distribution, we performed a meta-analysis of 16 genome-wide association studies (GWAS, N = 38,580) informative for adult waist circumference (WC) and waist-hip ratio (WHR). We selected 26 SNPs for follow-up, for which the evidence of association with measures of central adiposity (WC and/or WHR) was strong and disproportionate to that for overall adiposity or height. Follow-up studies in a maximum of 70,689 individuals identified two loci strongly associated with measures of central adiposity; these map near TFAP2B (WC, P = 1.9x10(-11)) and MSRA (WC, P = 8.9x10(-9)). A third locus, near LYPLAL1, was associated with WHR in women only (P = 2.6x10(-8)). The variants near TFAP2B appear to influence central adiposity through an effect on overall obesity/fat-mass, whereas LYPLAL1 displays a strong female-only association with fat distribution. By focusing on anthropometric measures of central obesity and fat distribution, we have identified three loci implicated in the regulation of human adiposity

Dynamics of a Josephson Array in a Resonant Cavity

We derive dynamical equations for a Josephson array coupled to a resonant cavity by applying the Heisenberg equations of motion to a model Hamiltonian described by us earlier [Phys. Rev. B {\bf 63}, 144522 (2001); Phys. Rev. B {\bf 64}, 179902 (E)]. By means of a canonical transformation, we also show that, in the absence of an applied current and dissipation, our model reduces to one described by Shnirman {\it et al} [Phys. Rev. Lett. {\bf 79}, 2371 (1997)] for coupled qubits, and that it corresponds to a capacitive coupling between the array and the cavity mode. From extensive numerical solutions of the model in one dimension, we find that the array locks into a coherent, periodic state above a critical number of active junctions, that the current-voltage characteristics of the array have self-induced resonant steps (SIRS's), that when $N_a$ active junctions are synchronized on a SIRS, the energy emitted into the resonant cavity is quadratic in $N_a$, and that when a fixed number of junctions is biased on a SIRS, the energy is linear in the input power. All these results are in agreement with recent experiments. By choosing the initial conditions carefully, we can drive the array into any of a variety of different integer SIRS's. We tentatively identify terms in the equations of motion which give rise to both the SIRS's and the coherence threshold. We also find higher-order integer SIRS's and fractional SIRS's in some simulations. We conclude that a resonant cavity can produce threshold behavior and SIRS's even in a one-dimensional array with appropriate experimental parameters, and that the experimental data, including the coherent emission, can be understood from classical equations of motion.Comment: 15 pages, 10 eps figures, submitted to Phys. Rev.

The bashful and the boastful : prestigious leaders and social change in Mesolithic Societies

The creation and maintenance of influential leaders and authorities is one of the key themes of archaeological and historical enquiry. However the social dynamics of authorities and leaders in the Mesolithic remains a largely unexplored area of study. The role and influence of authorities can be remarkably different in different situations yet they exist in all societies and in almost all social contexts from playgrounds to parliaments. Here we explore the literature on the dynamics of authority creation, maintenance and contestation in egalitarian societies, and discuss the implications for our interpretation and understanding of the formation of authorities and leaders and changing social relationships within the Mesolithic

Variation in Indonesian cocoa farm productivity in relation to management, environmental and edaphic factors

A survey was conducted of Indonesian cocoa farms to assess the extent of yield variation and factors associated with this variation. The survey of 120 farms during the course of three years encompassed four provinces in Sulawesi (South, South-East, West and Central), Western Sumatra, Lampung, East Java and West Papua. A high degree of yield variation was observed between farms, the average over three years ranged from 39 to 3586 kg ha-1. Overall, yields were greater on farms that were classified as “highly managed”, compared to “moderately” and “less managed”. Seasonal variability in yields was generally greater in districts with a more pronounced dry season such as South Sulawesi and Lampung. Multiple regression analyses revealed particular husbandry practices that were linked with higher cocoa yields. Specifically, the use of inorganic fertilisers, application of fungicides against blackpod and weeding were all practices that were associated with higher yields. A positive association between rainfall and yield was observed for the years 2014/15 and 2015/16 but not 2016/17, which was a La Niña year (when rainfall totals were higher). Some of the farms surveyed were planted with cocoa at very low densities implying an opportunity for yield improvement through gap filling or replanting at higher densities (although it was noted that some farmers maintained lower planting densities due to the cultivation of companion crops). Given the smallholder status of most cocoa farms in Indonesia (mean area in this study was 0.71 ha) it is important that farmers are able to maximise returns from their land in order to maintain a livelihood. This study illustrated the potential for yield improvement on Indonesian cocoa farms through adoption of best agronomic practice

Quantum Impurity Entanglement

Entanglement in J_1-J_2, S=1/2 quantum spin chains with an impurity is studied using analytic methods as well as large scale numerical density matrix renormalization group methods. The entanglement is investigated in terms of the von Neumann entropy, S=-Tr rho_A log rho_A, for a sub-system A of size r of the chain. The impurity contribution to the uniform part of the entanglement entropy, S_{imp}, is defined and analyzed in detail in both the gapless, J_2 <= J_2^c, as well as the dimerized phase, J_2>J_2^c, of the model. This quantum impurity model is in the universality class of the single channel Kondo model and it is shown that in a quite universal way the presence of the impurity in the gapless phase, J_2 <= J_2^c, gives rise to a large length scale, xi_K, associated with the screening of the impurity, the size of the Kondo screening cloud. The universality of Kondo physics then implies scaling of the form S_{imp}(r/xi_K,r/R) for a system of size R. Numerical results are presented clearly demonstrating this scaling. At the critical point, J_2^c, an analytic Fermi liquid picture is developed and analytic results are obtained both at T=0 and T>0. In the dimerized phase an appealing picure of the entanglement is developed in terms of a thin soliton (TS) ansatz and the notions of impurity valence bonds (IVB) and single particle entanglement (SPE) are introduced. The TS-ansatz permits a variational calculation of the complete entanglement in the dimerized phase that appears to be exact in the thermodynamic limit at the Majumdar-Ghosh point, J_2=J_1/2, and surprisingly precise even close to the critical point J_2^c. In appendices the relation between the finite temperature entanglement entropy, S(T), and the thermal entropy, S_{th}(T), is discussed and and calculated at the MG-point using the TS-ansatz.Comment: 62 pages, 27 figures, JSTAT macro