Quantum phase transitions in the Kondo-necklace model: Perturbative continuous unitary transformation approach

The Kondo-necklace model can describe magnetic low-energy limit of strongly correlated heavy fermion materials. There exist multiple energy scales in this model corresponding to each phase of the system. Here, we study quantum phase transition between the Kondo-singlet phase and the antiferromagnetic long-range ordered phase, and show the effect of anisotropies in terms of quantum information properties and vanishing energy gap. We employ the "perturbative continuous unitary transformations" approach to calculate the energy gap and spin-spin correlations for the model in the thermodynamic limit of one, two, and three spatial dimensions as well as for spin ladders. In particular, we show that the method, although being perturbative, can predict the expected quantum critical point, where the gap of low-energy spectrum vanishes, which is in good agreement with results of other numerical and Green's function analyses. In addition, we employ concurrence, a bipartite entanglement measure, to study the criticality of the model. Absence of singularities in the derivative of concurrence in two and three dimensions in the Kondo-necklace model shows that this model features multipartite entanglement. We also discuss crossover from the one-dimensional to the two-dimensional model via the ladder structure.Comment: 12 pages, 6 figure

Occurrence of Aflatoxin M1 in Milks of Five Animal Species in Iran: A Systematic Review and Meta-analysis

Consumption of milks contaminated with aflatoxin M1 (AFM1) may result in serious health problems in humans. In the present study, English and Persian electronic databases were comprehensively searched for publications from 2005 to 2018. Results indicated that pooled prevalence of AFM1 contamination in milks of buffalo, cow, sheep, goat, and camel were 86, 86, 42, 34, and 30%, respectively. Furthermore, average concentration of AFM1 were 78.73, 40.86, 26.71, 24.30, and 20.63 ng/L for milks in the same order. Therefore, continued monitoring of AFM1 contamination in milks and dairy foodstuffs deserves a serious governmental consideration