Symmetry-projected cluster mean-field theory applied to spin systems

We introduce $S_z$ spin-projection based on cluster mean-field theory and apply it to the ground state of strongly-correlated spin systems. In cluster mean-field, the ground state wavefunction is written as a factorized tensor product of optimized cluster states. In previous work, we have focused on unrestricted cluster mean-field, where each cluster is $S_z$ symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all $S_z$ sectors, breaking $S_z$ symmetry. In addition, a projection scheme is used to restore global $S_z$, which gives rise to $S_z$ spin-projected generalized cluster mean-field (S$_z$GcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D $J_1-J_2$ and $XXZ$ Heisenberg models. Our results indicate that the new methods (GcMF and S$_z$GcMF) provide a qualitative and semi-quantitative description of the Heisenberg lattices in the regimes considered, suggesting them as useful references for further inter-cluster correlations, which are discussed in this work

A cluster-based mean-field, perturbative and coupled-cluster theory description of strongly correlated systems

We introduce cluster-based mean-field, perturbation and coupled-cluster theories to describe the ground state of strongly-correlated spin systems. In cluster mean-field, the ground state wavefunction is written as a simple tensor product of optimized cluster states. The cluster-language and the mean-field nature of the ansatz allows for a straightforward improvement based on perturbation theory and coupled-cluster, to account for inter-cluster correlations. We present benchmark calculations on the 2D square $J_1-J_2$ Heisenberg model, using cluster mean-field, second-order perturbation theory and coupled-cluster. We also present an extrapolation scheme that allows us to compute thermodynamic limit energies very accurately. Our results indicate that, even with relatively small clusters, the correlated methods can provide an accurate description of the Heisenberg model in the regimes considered. Some ways to improve the results presented in this work are discussed

Creativity in the era of social networking: A case study in Tertiary Education in the Greek context.

This paper investigates the utilization of a social network tool in order to promote creativity in higher education. Buddypress was selected as a social network tool and de Bono’s “6 thinking hats” as a creativity strategy. The participants were 17 undergraduate students from a case study in a Univer-sity in Greece in the field of social sciences. Creativity was defined by Tor-rance & Ball’s [25] factors and the results were analyzed using authentic assessment and a questionnaire. The findings show that the research pro-cess was beneficial to students’ creativity and that social network tools can be utilized successfully with such a focus. These findings should be treated carefully in terms of generalizing them, as they were derived from a case study. This research could be useful to educators and researchers as a pio-neering approach in all levels of education

Construction and analytical applications of liquid-membrane electrodes for atropine and novatropine

Liquid-membrane electrodes sensitive to atropinium and novatropinium cations are described. The atropinium electrode exhibits rapid and near-Nernstian response in the 10-2-3 × 10-5 M range over the pH range 2-8.5; the novatropinium electrode shows near-Nernstian response in the 10-2-3 × 10-6 M range at pH 2-10. Other alkaloids interfere. Direct potentiometry and potentiometric titrations are used to determine atropine and novatropine in pharmaceutical preparations with satisfactory results. © 1981

Construction and analytical applications of liquid-membrane electrodes for atropine and novatropine

Liquid-membrane electrodes sensitive to atropinium and novatropinium cations are described. The atropinium electrode exhibits rapid and near-Nernstian response in the 10-2-3 × 10-5 M range over the pH range 2-8.5; the novatropinium electrode shows near-Nernstian response in the 10-2-3 × 10-6 M range at pH 2-10. Other alkaloids interfere. Direct potentiometry and potentiometric titrations are used to determine atropine and novatropine in pharmaceutical preparations with satisfactory results. © 1981