Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

Entanglement of excited states in critical spin chains

Renyi and von Neumann entropies quantifying the amount of entanglement in ground states of critical spin chains are known to satisfy a universal law which is given by the conformal field theory (CFT) describing their scaling regime. This law can be generalized to excitations described by primary fields in CFT, as was done by Alcaraz et al in 2011 (see reference [1], of which this work is a completion). An alternative derivation is presented, together with numerical verifications of our results in different models belonging to the c = 1, 1/2 universality classes. Oscillations of the Renyi entropy in excited states are also discussed.

Universal behavior of the Shannon mutual information of critical quantum chains

We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly c of the underlying conformal field theory governing the long-distance physics of the quantum chain. We study analytically a chain of coupled harmonic oscillators and numerically the Q-state Potts models (Q = 2, 3, and 4), the XXZ quantum chain, and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes, its finite-size behavior already detects the universality class of quantum critical behavior.

An investigation about Brazilian mango and grape exports

Purpose - The objective of this paper is to characterise the transactions between European buyers and Brazilian mango and grape producers. Design/methodology/approach - The method selected for this paper was multiple case studies. The Brazilian mango and grape supply chains' export activities to Europe were investigated. The field research was undertaken in Brazil, Germany, The Netherlands and the UK. In total, 41 face-to-face interviews were carried out. Findings - The supermarkets' literature tends to generalise the strategies of retailers focusing on differentiation and preferred suppliers. However, in empirical research conducted in the UK, Germany and The Netherlands it is possible to conclude that the procurement strategies of supermarkets can vary sharply. The results reveal the presence of different agents who demand different quality standards. The level of intensity depends on consumer behaviour, the features of product commercialised and the characteristics of the production segment in each country. Research limitations/implications - First, in relation to the empirical method there is a limitation because the case study does not allow statistical generalisation. Consequently, it will be interesting to undertake quantitative research in order to quantify the variables presented and their impact on the structure of value chains. Second, the research focuses only on two stages of the supply chain, producers and buyers. Practical implications - The differences between UK and German supermarkets challenge the supermarket literature, which tends to generalise the strategies of retailers focusing on differentiation and preferred suppliers. Originality/value - The study shows that the issue of influence and activities of retail agents along the value chain can be analysed taking several variables into consideration: the products commercialised; the distribution segment; and the consumer market. This result opens the way for analysing different structures of the value chain and the impact of these differences on the entry of producers for developing countries into the global market.

The role of empirical research in the study of complex forms of governance in agroindustrial systems

The growing complexity of supply chains poses new challenges for Agricultural Research Centers and statistical agencies. The aim of this perspective paper is to discuss the role of empirical research in understanding the complex forms of governance in agribusiness. The authors argue that there are three fundamental levels of analysis: (i) the basic structure of the market, (ii) the formal contractual arrangements that govern relations within the agroindustrial system and (iii) the transactional dimensions governed by non-contractual means. The case of the agrochemical industry in Brazil illustrates how traditional analyses that only address market structure are insufficient to fully explain the agricultural sector and its supply chain. The article concludes by suggesting some indicators which could be collected by statistical agencies to improve understanding of the complex relationships among agribusiness segments. In doing so, the paper seeks to minimize costs and to enable a better formulation of public and private policies.

Sustentabilidade e cadeia de suprimentos: uma perspectiva comparada de publicações nacionais e internacionais

O objetivo do artigo é apresentar um quadro de referência de conceitos da Gestão da Sustentabilidade na Cadeia de Suprimentos (GSCS) para auxiliar pesquisas futuras na tentativa de integração intra e interorganizacional fundamentada em aspectos da sustentabilidade. Trata-se de um artigo teórico, cujo procedimento metodológico adotado foi o desk research em periódicos da área de gestão e operações, realizado em duas etapas. Na primeira, buscou-se visualizar os estudos da temática em seis importantes periódicos internacionais da área, totalizando 53 artigos entre 1954 e 2009. Esta etapa gerou uma evolução da temática, contribuindo para apontar tendências. Na segunda, foram revisados seis periódicos nacionais da área de administração. Selecionaram-se 11 artigos, publicados entre 1961 e 2009, resultando em um panorama da temática no contexto acadêmico brasileiro. O conceito de GSCS apareceu apenas em 2007, o que mostra a atualidade do tema, embora este seja a junção de temáticas anteriormente estudadas.

Dissipation effects in random transverse-field Ising chains

We study the effects of Ohmic, super-Ohmic, and sub-Ohmic dissipation on the zero-temperature quantum phase transition in the random transverse-field Ising chain by means of an (asymptotically exact) analytical strong-disorder renormalization-group approach. We find that Ohmic damping destabilizes the infinite-randomness critical point and the associated quantum Griffiths singularities of the dissipationless system. The quantum dynamics of large magnetic clusters freezes completely, which destroys the sharp phase transition by smearing. The effects of sub-Ohmic dissipation are similar and also lead to a smeared transition. In contrast, super-Ohmic damping is an irrelevant perturbation; the critical behavior is thus identical to that of the dissipationless system. We discuss the resulting phase diagrams, the behavior of various observables, and the implications to higher dimensions and experiments.

Rounding of a first-order quantum phase transition to a strong-coupling critical point

We investigate the effects of quenched disorder on first-order quantum phase transitions on the example of the N-color quantum Ashkin-Teller model. By means of a strong-disorder renormalization group, we demonstrate that quenched disorder rounds the first-order quantum phase transition to a continuous one for both weak and strong coupling between the colors. In the strong-coupling case, we find a distinct type of infinite-randomness critical point characterized by additional internal degrees of freedom. We investigate its critical properties in detail and find stronger thermodynamic singularities than in the random transverse field Ising chain. We also discuss the implications for higher spatial dimensions as well as unusual aspects of our renormalization-group scheme. DOI: 10.1103/PhysRevB.86.214204