Quantum Phase Transitions and the Extended Coupled Cluster Method

We discuss the application of an extended version of the coupled cluster method to systems exhibiting a quantum phase transition. We use the lattice O(4) non-linear sigma model in (1+1)- and (3+1)-dimensions as an example. We show how simple predictions get modified, leading to the absence of a phase transition in (1+1) dimensions, and strong indications for a phase transition in (3+1) dimensions

High-Order Coupled Cluster Method Calculations for the Ground- and Excited-State Properties of the Spin-Half XXZ Model

In this article, we present new results of high-order coupled cluster method (CCM) calculations, based on a N\'eel model state with spins aligned in the $z$-direction, for both the ground- and excited-state properties of the spin-half {\it XXZ} model on the linear chain, the square lattice, and the simple cubic lattice. In particular, the high-order CCM formalism is extended to treat the excited states of lattice quantum spin systems for the first time. Completely new results for the excitation energy gap of the spin-half {\it XXZ} model for these lattices are thus determined. These high-order calculations are based on a localised approximation scheme called the LSUB$m$ scheme in which we retain all $k$-body correlations defined on all possible locales of $m$ adjacent lattice sites ($k \le m$). The ``raw'' CCM LSUB$m$ results are seen to provide very good results for the ground-state energy, sublattice magnetisation, and the value of the lowest-lying excitation energy for each of these systems. However, in order to obtain even better results, two types of extrapolation scheme of the LSUB$m$ results to the limit $m \to \infty$ (i.e., the exact solution in the thermodynamic limit) are presented. The extrapolated results provide extremely accurate results for the ground- and excited-state properties of these systems across a wide range of values of the anisotropy parameter.Comment: 31 Pages, 5 Figure

The Extended Coupled Cluster Treatment of Correlations in Quantum Magnets

The spin-half XXZ model on the linear chain and the square lattice are examined with the extended coupled cluster method (ECCM) of quantum many-body theory. We are able to describe both the Ising-Heisenberg phase and the XY-Heisenberg phase, starting from known wave functions in the Ising limit and at the phase transition point between the XY-Heisenberg and ferromagnetic phases, respectively, and by systematically incorporating correlations on top of them. The ECCM yields good numerical results via a diagrammatic approach, which makes the numerical implementation of higher-order truncation schemes feasible. In particular, the best non-extrapolated coupled cluster result for the sublattice magnetization is obtained, which indicates the employment of an improved wave function. Furthermore, the ECCM finds the expected qualitatively different behaviours of the linear chain and the square lattice cases.Comment: 22 pages, 3 tables, and 15 figure

Steady state existence of passive vector fields under the Kraichnan model

The steady state existence problem for Kraichnan advected passive vector models is considered for isotropic and anisotropic initial values in arbitrary dimension. The model includes the magnetohydrodynamic (MHD) equations, linear pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition to reproducing the previously known results for the MHD and linear pressure model, we obtain the values of the Kraichnan model roughness parameter $\xi$ for which the LNS steady state exists.Comment: Improved text & figures, added references & other correction

Incomegetting and Environmental Degradation

Drawing on Alfred Schütz’s thought, as well as on a number of modern pragmatists and practice theorists, we theorize incomegetting—referring to practices of getting income, typically salaried work—as the paramount structurer of everyday life and, therefore, also the chief mediator of the human–nature metabolism. Even though the pragmatics of everyday life as an aggregate underlie the bulk of environmental impacts, these insidious impacts impose little immediate influence on everyday life, in particular in the urban Global North. In other words, the pragmatic dimension of everyday activities—principally, work—that takes place within a vastly complex and globally interlinked productive world system, has most often no immediate connection to the “natural” environment. While parts of the populations are directly dependent in terms of livelihoods on the “natural” environment, these populations are typically pushed to the margins of the global productive system. The understanding formulated in this essay suggests that in environmental social sciences there is a reason to shift the epicenter of the analysis from consumption to everyday life, to the varied practices of incomegetting. Against the backdrop of this paper, universal basic income schemes ought to have radical impacts on the way we relate also to the “natural” environment and such schemes necessitate understanding the essence of money in our contemporary realities

Incomegetting and Environmental Degradation

Drawing on Alfred Schütz’s thought, as well as on a number of modern pragmatists and practice theorists, we theorize incomegetting—referring to practices of getting income, typically salaried work—as the paramount structurer of everyday life and, therefore, also the chief mediator of the human–nature metabolism. Even though the pragmatics of everyday life as an aggregate underlie the bulk of environmental impacts, these insidious impacts impose little immediate influence on everyday life, in particular in the urban Global North. In other words, the pragmatic dimension of everyday activities—principally, work—that takes place within a vastly complex and globally interlinked productive world system, has most often no immediate connection to the “natural” environment. While parts of the populations are directly dependent in terms of livelihoods on the “natural” environment, these populations are typically pushed to the margins of the global productive system. The understanding formulated in this essay suggests that in environmental social sciences there is a reason to shift the epicenter of the analysis from consumption to everyday life, to the varied practices of incomegetting. Against the backdrop of this paper, universal basic income schemes ought to have radical impacts on the way we relate also to the “natural” environment and such schemes necessitate understanding the essence of money in our contemporary realities

Electrons and positrons in metal vacancies

The electron density profiles at monovacancies of simple metals are calculated by the self-consistent Kohn-Sham method and by a number of statistical methods. The metal is described by a uniform positive background charge together with an interacting electron gas, and the vacancy is approximated as a spherical hole in the background. The Kohn-Sham electron density inside the vacancy is found to be in average 15 of the density in the bulk material. Of the various statistical methods, the simple Thomas-Fermi approximation is found to describe best the average electron density over the whole metallic density range when compared to the Kohn-Sham results. The energies of vacancy formation are calculated by using the Kohn-Sham electron densities together with three lattice models, and reasonable numerical success is achieved for alkali metals. In the case of polyvalent metals the results are not satisfactory even if the uniform background were replaced by point ions or if the electron-ion interactions were described by Ashcroft empty-core pseudopotentials. The lifetimes of a positron trapped at the vacancies of several metals are calculated by using both the Kohn-Sham and the Thomas-Fermi electron densities. The results for most metals are in agreement with experimental values. The angular-correlation curve of the positron in aluminum vacancy is calculated directly from the Kohn-Sham one-electron wave functions. The result agrees with the curve calculated from the so-called mixed-density approximation and also with the experimental result.Peer reviewe