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

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

Enhanced Bound State Formation in Two Dimensions via Stripe-Like Hopping Anisotropies

We have investigated two-electron bound state formation in a square two-dimensional t-J-U model with hopping anisotropies for zero electron density; these anisotropies are introduced to mimic the hopping energies similar to those expected in stripe-like arrangements of holes and spins found in various transition metal oxides. In this report we provide analytical solutions to this problem, and thus demonstrate that bound-state formation occurs at a critical exchange coupling, J_c, that decreases to zero in the limit of extreme hopping anisotropy t_y/t_x -> 0. This result should be contrasted with J_c/t = 2 for either a one-dimensional chain, or a two-dimensional plane with isotropic hopping. Most importantly, this behaviour is found to be qualitatively similar to that of two electrons on the two-leg ladder problem in the limit of t_interchain/t_intrachain -> 0. Using the latter result as guidance, we have evaluated the pair correlation function, thus determining that the bound state corresponds to one electron moving along one chain, with the second electron moving along the opposite chain, similar to two electrons confined to move along parallel, neighbouring, metallic stripes. We emphasize that the above results are not restricted to the zero density limit - we have completed an exact diagonalization study of two holes in a 12 X 2 two-leg ladder described by the t-J model and have found that the above-mentioned lowering of the binding energy with hopping anisotropy persists near half filling.Comment: 6 pages, 3 eps figure

An Exact Diagonalization Demonstration of Incommensurability and Rigid Band Filling for N Holes in the t-J Model

We have calculated S(q) and the single particle distribution function for N holes in the t - J model on a non--square sqrt{8} X sqrt{32} 16--site lattice with periodic boundary conditions; we justify the use of this lattice in compariosn to those of having the full square symmetry of the bulk. This new cluster has a high density of vec k points along the diagonal of reciprocal space, viz. along k = (k,k). The results clearly demonstrate that when the single hole problem has a ground state with a system momentum of vec k = (pi/2,pi/2), the resulting ground state for N holes involves a shift of the peak of the system's structure factor away from the antiferromagnetic state. This shift effectively increases continuously with N. When the single hole problem has a ground state with a momentum that is not equal to k = (pi/2,pi/2), then the above--mentioned incommensurability for N holes is not found. The results for the incommensurate ground states can be understood in terms of rigid--band filling: the effective occupation of the single hole k = (pi/2,pi/2) states is demonstrated by the evaluation of the single particle momentum distribution function . Unlike many previous studies, we show that for the many hole ground state the occupied momentum states are indeed k = (+/- pi/2,+/- pi/2) states.Comment: Revtex 3.0; 23 pages, 1 table, and 13 figures, all include

Sr impurity effects on the magnetic correlations of LaSrCuO

We examine the low-temperature magnetic properties of moderately doped LaSrCuO paying particular attention to the spin-glass (SG) phase and the C-IC transition as they are affected by Sr impurity disorder. New measurements of the low-temperature susceptibility in the SG phase show an increase of an anomalously small Curie constant with doping. This behaviour is explained in terms of our theoretical work that finds small clusters of AFM correlated regions separated by disordered domain walls. The domain walls lead to a percolating sequence of paths connecting the impurities. We predict that for this spin morphology the Curie constant should scale as $1/(2 \xi(x,T=0)^2)$, a result that is quantitatively in agreement with experiment. Also, we find that the magnetic correlations in the ground states in the SG phase are commensurate, and that this behaviour should persist at higher temperatures where the holes should move along the domain walls. However, our results show that incommensurate correlations develop continuously around 5 % doping, consistent with recent measurements by Yamada.Comment: 30 pages, revtex, 8 .ps format figures (2 meant to be in colour), to be published in Physical Review B

A robust DNA interface on a silicon electrode

Two different interfaces prepared via UV-hydrosilylation of undecylenic acid and 1,8-nonadiyne on silicon(111) have been explored to develop a robust electrochemical DNA sensor. Electrodes modified with undecylenic acid were found to stably immobilise DNA but could not resist the growth of insulating oxides, whereas 1,8-nonadiyne modified electrodes satisfy both requirements

Spin and Charge Texture around In-Plane Charge Centers in the CuO_2 planes

Recent experiments on La_2Cu_{1-x}Li_xO_4 show that although the doped holes remain localized near the substitutional Li impurities, magnetic order is rapidly suppressed. An examination of the spin texture around a bound hole in a CuO_2 plane shows that the formation of a skyrmion is favored in a wide range of parameters, as was previously proposed in the context of Sr doping. The spin texture may be observable by elastic diffuse neutron scattering, and may also have a considerable effect on NMR lineshapes.Comment: 4 pages, postscript file, hardcopy available upon request, to appear in PR

Analyzing the success of T-matrix diagrammatic theories in representing a modified Hubbard model

We present a systematic study of various forms of renormalization that can be applied in the calculation of the self-energy of the Hubbard model within the T-matrix approximation. We compare the exact solutions of the attractive and repulsive Hubbard models, for linear chains of lengths up to eight sites, with all possible taxonomies of the T-matrix approximation. For the attractive Hubbard model, the success of a minimally self-consistent theory found earlier in the atomic limit (Phys. Rev. B 71, 155111 (2005)) is not maintained for finite clusters unless one is in the very strong correlation limit. For the repulsive model, in the weak correlation limit at low electronic densities -- that is, where one would expect a self-consistent T-matrix theory to be adequate -- we find the fully renormalized theory to be most successful. In our studies we employ a modified Hubbard interaction that eliminates all Hartree diagrams, an idea which was proposed earlier (Phys. Rev. B 63, 035104 (2000)).Comment: Includes modified discussion of 1st-order phase transition. Accepted for publication in J. Phys.: Condensed Matte

Electronic properties of disordered corner-sharing tetrahedral lattices

We have examined the behaviour of noninteracting electrons moving on a corner-sharing tetrahedral lattice into which we introduce a uniform (box) distribution, of width W, of random on-site energies. We have used both the relative localization length and the spectral rigidity to analyze the nature of the eigenstates, and have determined both the mobility edge trajectories as a function of W, and the critical disorder, Wc, beyond which all states are localized. We find (i) that the mobility edge trajectories (energies Ec vs. disorder W) are qualitatively different from those found for a simple cubic lattice, and (ii) that the spectral rigidity is scale invariant at Wc and thus provides a reliable method of estimating this quantity -- we find Wc/t=14.5. We discuss our results in the context of the metal-to-insulator transition undergone by LiAlyTi{2-y}O4 in a quantum site percolation model that also includes the above-mentioned Anderson disorder, and show that the effects produced by Anderson disorder are far less important than those produced by quantum site percolation, at least in the determination of the doping concentration at which the metal-to-insulator transition is predicted to occur