Application of a multi-site mean-field theory to the disordered Bose-Hubbard model

We present a multi-site formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with inter-cluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multi-site formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose glass-to-superfluid transition, one an approximation based on the behaviour of the condensate fraction, and one of which relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non self-averaging is discussed.Comment: Accepted for publication in Physical Review

Multi-site mean-field theory for cold bosonic atoms in optical lattices

We present a detailed derivation of a multi-site mean-field theory (MSMFT) used to describe the Mott-insulator to superfluid transition of bosonic atoms in optical lattices. The approach is based on partitioning the lattice into small clusters which are decoupled by means of a mean field approximation. This approximation invokes local superfluid order parameters defined for each of the boundary sites of the cluster. The resulting MSMFT grand potential has a non-trivial topology as a function of the various order parameters. An understanding of this topology provides two different criteria for the determination of the Mott insulator superfluid phase boundaries. We apply this formalism to $d$-dimensional hypercubic lattices in one, two and three dimensions, and demonstrate the improvement in the estimation of the phase boundaries when MSMFT is utilized for increasingly larger clusters, with the best quantitative agreement found for $d=3$. The MSMFT is then used to examine a linear dimer chain in which the on-site energies within the dimer have an energy separation of $\Delta$. This system has a complicated phase diagram within the parameter space of the model, with many distinct Mott phases separated by superfluid regions.Comment: 30 pages, 23 figures, accepted for publication in Phys. Rev.

Optical conductivity of a metal-insulator transition for the Anderson-Hubbard model in 3 dimensions away from 1/2 filling

We have completed a numerical investigation of the Anderson-Hubbard model for three-dimensional simple cubic lattices using a real-space self-consistent Hartree-Fock decoupling approximation for the Hubbard interaction. In this formulation we treat the spatial disorder exactly, and therefore we account for effects arising from localization physics. We have examined the model for electronic densities well away 1/2 filling, thereby avoiding the physics of a Mott insulator. Several recent studies have made clear that the combined effects of electronic interactions and spatial disorder can give rise to a suppression of the electronic density of states, and a subsequent metal-insulator transition can occur. We augment such studies by calculating the ac conductivity for such systems. Our numerical results show that weak interactions enhance the density of states at the Fermi level and the low-frequency conductivity, there are no local magnetic moments, and the ac conductivity is Drude-like. However, with a large enough disorder strength and larger interactions the density of states at the Fermi level and the low-frequency conductivity are both suppressed, the conductivity becomes non-Drude-like, and these phenomena are accompanied by the presence of local magnetic moments. The low-frequency conductivity changes from a sigma-sigma_dc omega^{1/2} behaviour in the metallic phase, to a sigma omega^2 behaviour in the nonmetallic regime. Our numerical results show that the formation of magnetic moments is essential to the suppression of the density of states at the Fermi level, and therefore essential to the metal-insulator transition

The myth of the new: Mass digitization, distant reading, and the future of the book

This article presents the theoretical background to a wider project that is attempting to increase our understanding of the impact and uses of large-scale digitization, being undertaken by the first author at University College London with the working title ‘What is the impact of large-scale digitization upon researchers and the information sector?’ It discusses the controversy surrounding the emergence of mass digitization: the creation and collection of huge resources containing millions of pages of textual cultural content. It demonstrates that the polarized nature of the literature about this technological development is far from unprecedented, and in fact can be traced through the theory of a number of varied fields: the debate surrounding mechanization and digital technologies, our understanding of the role of the sublime in modern representations of technology, the similarities between the sociology of city life and digital information overload, and the way in which innovations are diffused throughout society. It proposes that these theories explain why debates around technological innovation often become so hyperbolic, creating an almost mythological view of technological determination. It concludes that, as a result of the processes outlined in this theory, mass digitization has become stuck between two conflicting rhetorical movements, and that it is therefore necessary to begin working to increase our understanding of this technology and to move the debate onwards using evidence from the real world

Dynamical properties of the single--hole tt--JJ model on a 32--site square lattice

We present results of an exact diagonalization calculation of the spectral function $A(\bf k, \omega)$ for a single hole described by the $t$--$J$ model propagating on a 32--site square cluster. The minimum energy state is found at a crystal momentum ${\bf k} = ({\pi\over 2}, {\pi\over 2})$, consistent with theory, and our measured dispersion relation agrees well with that determined using the self--consistent Born approximation. In contrast to smaller cluster studies, our spectra show no evidence of string resonances. We also make a qualitative comparison of the variation of the spectral weight in various regions of the first Brillouin zone with recent ARPES data.Comment: 10 pages, 5 postscript figures include

The influence of foliar diseases, and their control by fungicides, on the protein concentration in wheat grain:a review

Experiments investigating effects of foliar disease control on wheat grain protein concentration (GPC) are reviewed. Fungicidal control of rusts (Puccinia spp.) and powdery mildew (Erysiphe graminis) increased or had no significant effect on GPC in almost all cases, whilst control of the Septoria spp. often resulted in reduced GPC, but with exceptions. Reasons for these differences are discussed with reference to host pathogen interactions. Irrespective of infection strategy (biotrophic or necrotrophic), controlling severe infection increased nitrogen yield and the proportion of above-ground crop nitrogen that was partitioned to the grain. Similar effects are recorded for above-ground biomass and dry matter harvest index. The relationships between fungicide effects on green flag leaf area duration (GFLAD) and GPC were examined and shown to be unaffected by mode of action of the fungicide. Interactions between fungicide use and cultivar, nitrogen and growing season are related to the amount and type of pathogen present, and environment. An economic analysis demonstrated that fungicide effects on GPC should not affect the choice of fungicide or application programme, but that applications of foliar urea at the start of grain filling can deliver a cost-effective method of eliminating GPC reductions that may occasionally result from fungicide use.authorsversionPeer reviewe