On the correct continuum limit of the functional-integral representation for the four-slave-boson approach to the Hubbard model: Paramagnetic phase

The Hubbard model with finite on-site repulsion U is studied via the functional-integral formulation of the four-slave-boson approach by Kotliar and Ruckenstein. It is shown that a correct treatment of the continuum imaginary time limit (which is required by the very definition of the functional integral) modifies the free energy when fluctuation (1/N) corrections beyond mean-field are considered. Our analysis requires us to suitably interpret the Kotliar and Ruckenstein choice for the bosonic hopping operator and to abandon the commonly used normal-ordering prescription, in order to obtain meaningful fluctuation corrections. In this way we recover the exact solution at U=0 not only at the mean-field level but also at the next order in 1/N. In addition, we consider alternative choices for the bosonic hopping operator and test them numerically for a simple two-site model for which the exact solution is readily available for any U. We also discuss how the 1/N expansion can be formally generalized to the four-slave-boson approach, and provide a simplified prescription to obtain the additional terms in the free energy which result at the order 1/N from the correct continuum limit.Comment: Changes: Printing problems (due to non-standard macros) have been removed, 44 page

Variational Cluster Perturbation Theory for Bose-Hubbard models

We discuss the application of the variational cluster perturbation theory (VCPT) to the Mott-insulator--to--superfluid transition in the Bose-Hubbard model. We show how the VCPT can be formulated in such a way that it gives a translation invariant excitation spectrum -- free of spurious gaps -- despite the fact that if formally breaks translation invariance. The phase diagram and the single-particle Green function in the insulating phase are obtained for one-dimensional systems. When the chemical potential of the cluster is taken as a variational parameter, the VCPT reproduces the dimension dependence of the phase diagram even for one-site clusters. We find a good quantitative agreement with the results of the density-matrix renormalization group when the number of sites in the cluster becomes of order 10. The extension of the method to the superfluid phase is discussed.Comment: v1) 10 pages, 6 figures. v2) Final version as publishe

Effects of increased salinity and an introduced predator on lowland amphibians in southern China: species identity matters

abstract no. V-01-9Approximately 30% of amphibian species are threatened due to a variety of factors affecting their habitats and physiology, yet contributions that interactions among factors make to population declines are not well-explored. Two factors, introduced mosquitofish (Gambusia affinis) and increased salinity, may coincide in lowland habitats used by breeding amphibians. Mosquitofish have been introduced worldwide and can be significant predators of amphibian larvae. Salinization of wetlands is an increasing problem globally due to (1) application of road deicing salts in temperate regions, (2) irrigation practices associated with intensive agriculture, particularly in Australia, and (3) saltwater intrusion due to sea-level rise. We investigated the effects of mosquitofish (Gambusia affinis) and increasing salinity on five species of lowland wetland-breeding amphibians from southern China. We exposed anuran hatchlings to four salinity levels and two fish treatments and all combinations of the two factors in a series of experiments. Four of the species were susceptible to predation by mosquitofish, two were sensitive to increased salinity at concentrations >6% seawater, and one was tolerant of both increased salinity and mosquitofish. We found no interaction between the predator and increased salinity. Salinization and mosquitofish represent significant threats to lowland amphibians in this region and, coupled with the ongoing loss and degradation of lowland wetlands, portend a bleak future for lowland amphibian populations in the region.postprintThe 49th Annual Meeting of the Association for Tropical Biology and Conservation (ATBC 2010), Bali, Indonesia, 19-23 July 2010. In Abstract Book of the 49th ATBC Annual Meeting, 2010, p.