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TomonagaâLuttinger liquid behavior and spinon confinement in YbAlO 3
Low dimensional quantum magnets are interesting because of the emerging collective behavior arising from strong quantum fluctuations. The one-dimensional (1D) Sâ=â1/2 Heisenberg antiferromagnet is a paradigmatic example, whose low-energy excitations, known as spinons, carry fractional spin Sâ=â1/2. These fractional modes can be reconfined by the application of a staggered magnetic field. Even though considerable progress has been made in the theoretical understanding of such magnets, experimental realizations of this low-dimensional physics are relatively rare. This is particularly true for rare-earth-based magnets because of the large effective spin anisotropy induced by the combination of strong spinâorbit coupling and crystal field splitting. Here, we demonstrate that the rare-earth perovskite YbAlO3 provides a realization of a quantum spin Sâ=â1/2 chain material exhibiting both quantum critical TomonagaâLuttinger liquid behavior and spinon confinementâdeconfinement transitions in different regions of magnetic fieldâtemperature phase diagram
PSA based multi objective evolutionary algorithms
It has generally been acknowledged that both proximity to the Pareto front and a certain diversity along the front, should be targeted when using evolutionary multiobjective optimization. Recently, a new partitioning mechanism, the Part and Select Algorithm (PSA), has been introduced. It was shown that this partitioning allows for the selection of a well-diversified set out of an arbitrary given set, while maintaining low computational cost. When embedded into an evolutionary search (NSGA-II), the PSA has significantly enhanced the exploitation of diversity. In this paper, the ability of the PSA to enhance evolutionary multiobjective algorithms (EMOAs) is further investigated. Two research directions are explored here. The first one deals with the integration of the PSA within an EMOA with a novel strategy. Contrary to most EMOAs, that give a higher priority to proximity over diversity, this new strategy promotes the balance between the two. The suggested algorithm allows some dominated solutions to survive, if they contribute to diversity. It is shown that such an approach substantially reduces the risk of the algorithm to fail in finding the Pareto front. The second research direction explores the use of the PSA as an archiving selection mechanism, to improve the averaged Hausdorff distance obtained by existing EMOAs. It is shown that the integration of the PSA into NSGA-II-I and Πp -EMOA as an archiving mechanism leads to algorithms that are superior to base EMOAS on problems with disconnected Pareto fronts. © 2014 Springer International Publishing Switzerland
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