Efficient implementation of the Gutzwiller variational method

We present a self-consistent numerical approach to solve the Gutzwiller variational problem for general multi-band models with arbitrary on-site interaction. The proposed method generalizes and improves the procedure derived by Deng et al., Phys. Rev. B. 79 075114 (2009), overcoming the restriction to density-density interaction without increasing the complexity of the computational algorithm. Our approach drastically reduces the problem of the high-dimensional Gutzwiller minimization by mapping it to a minimization only in the variational density matrix, in the spirit of the Levy and Lieb formulation of DFT. For fixed density the Gutzwiller renormalization matrix is determined as a fixpoint of a proper functional, whose evaluation only requires ground-state calculations of matrices defined in the Gutzwiller variational space. Furthermore, the proposed method is able to account for the symmetries of the variational function in a controlled way, reducing the number of variational parameters. After a detailed description of the method we present calculations for multi-band Hubbard models with full (rotationally invariant) Hund's rule on-site interaction. Our analysis shows that the numerical algorithm is very efficient, stable and easy to implement. For these reasons this method is particularly suitable for first principle studies -- e.g., in combination with DFT -- of many complex real materials, where the full intra-atomic interaction is important to obtain correct results.Comment: 19 pages, 7 figure

The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition

We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first order transition line and its second order critical end point. The critical point is shown to be a cusp catastrophe in the parameter space, opening a pitchfork bifurcation along the first order transition line, while the hysteresis boundaries are shown to be saddle-node bifurcations of two merging fixpoints. Using Landau theory the properties of the critical end point is determined and related to the critical eigenmode of the Jacobian. Our findings provide new insights into basic properties of this intensively studied transition.Comment: 11 pages, 12 figures, 1 tabl

Electron-hole pairs during the adsorption dynamics of O2 on Pd(100) - Exciting or not?

During the exothermic adsorption of molecules at solid surfaces dissipation of the released energy occurs via the excitation of electronic and phononic degrees of freedom. For metallic substrates the role of the nonadiabatic electronic excitation channel has been controversially discussed, as the absence of a band gap could favour an easy coupling to a manifold of electronhole pairs of arbitrarily low energies. We analyse this situation for the highly exothermic showcase system of molecular oxygen dissociating at Pd(100), using time-dependent perturbation theory applied to first-principles electronic-structure calculations. For a range of different trajectories of impinging O2 molecules we compute largely varying electron-hole pair spectra, which underlines the necessity to consider the high-dimensionality of the surface dynamical process when assessing the total energy loss into this dissipation channel. Despite the high Pd density of states at the Fermi level, the concomitant non-adiabatic energy losses nevertheless never exceed about 5% of the available chemisorption energy. While this supports an electronically adiabatic description of the predominant heat dissipation into the phononic system, we critically discuss the non-adiabatic excitations in the context of the O2 spin transition during the dissociation process.Comment: 20 pages including 7 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.html [added two references, changed V_{fsa} to V_{6D}, modified a few formulations in interpretation of spin asymmetry of eh-spectra, added missing equals sign in Eg.(2.10)

Forces on Dust Grains Exposed to Anisotropic Interstellar Radiation Fields

Grains exposed to anisotropic radiation fields are subjected to forces due to the asymmetric photon-stimulated ejection of particles. These forces act in addition to the ``radiation pressure'' due to absorption and scattering. Here we model the forces due to photoelectron emission and the photodesorption of adatoms. The ``photoelectric'' force depends on the ambient conditions relevant to grain charging. We find that it is comparable to the radiation pressure when the grain potential is relatively low and the radiation spectrum is relatively hard. The calculation of the ``photodesorption'' force is highly uncertain, since the surface physics and chemsitry of grain materials are poorly understood at present. For our simple yet plausible model, the photodesorption force dominates the radiation pressure for grains with size >~0.1 micron exposed to starlight from OB stars. We find that the anisotropy of the interstellar radiation field is ~10% in the visible and ultraviolet. We estimate size-dependent drift speeds for grains in the cold and warm neutral media and find that micron-sized grains could potentially be moved across a diffuse cloud during its lifetime.Comment: LaTeX(41 pages, 19 figures), submitted to Ap

Model study of adsorbed metallic quantum dots: Na on Cu(111)

We model electronic properties of the second monolayer Na adatom islands (quantum dots) on the Cu(111) surface covered homogeneously by the first Na monolayer. An axially-symmetric three-dimensional jellium model, taking into account the effects due to the first Na monolayer and the Cu substrate, has been developed. The electronic structure is solved within the local-density approximation of the density-functional theory using a real-space multigrid method. The model enables the study of systems consisting of thousands of Na-atoms. The results for the local density of states are compared with differential conductance ($dI/dV$) spectra and constant current topographs from Scanning Tunneling Microscopy.Comment: 10 pages, 8 figures. For better quality figures, download http://www.fyslab.hut.fi/~tto/cylart1.pd

Role of bulk and surface phonons in the decay of metal surface states

We present a comprehensive theoretical investigation of the electron-phonon contribution to the lifetime broadening of the surface states on Cu(111) and Ag(111), in comparison with high-resolution photoemission results. The calculations, including electron and phonon states of the bulk and the surface, resolve the relative importance of the Rayleigh mode, being dominant for the lifetime at small hole binding energies. Including the electron-electron interaction, the theoretical results are in excellent agreement with the measured binding energy and temperature dependent lifetime broadening.Comment: 4 pages, 3 figure

Effectiveness and cost-effectiveness of a self-guided internet intervention for social anxiety symptoms in a general population sample : randomized controlled trial

Background: Many people are accessing digital self-help for mental health problems, often with little evidence of effectiveness.Social anxiety is one of the most common sources of mental distress in the population and many people with symptoms do not seek help for what represents a significant public health problem. Objective: Two group randomized controlled trial conducted in England between 11th May 2016 and 27th June 2018. Adults with social anxiety symptoms who were not receiving treatment for social anxiety were recruited using online advertisements. All participants had unrestricted access to usual care and were randomized in a 1:1 ratio to either a web-based unguided self-help intervention based on cognitive-behavioural principles, or to a waiting list control group. All outcomes were collected through self-report online questionnaires. The primary outcome was the change in 17-item self-report Social Phobia Inventory (SPIN-17) score from baseline to 6 weeks using a linear mixed-effect model that used data from all timepoints (6 weeks, 3, 6, 12 months). Methods: Two group randomized controlled trial conducted in England between 11th May 2016 and 27th June 2018. Adults with social anxiety symptoms who were not receiving treatment for social anxiety were recruited using online advertisements. All participants had unrestricted access to usual care and were randomized in a 1:1 ratio to either a web-based unguided self-help intervention based on cognitive-behavioural principles, or to a waiting list control group. All outcomes were collected through self-report online questionnaires. The primary outcome was the change in 17-item self-report Social Phobia Inventory (SPIN-17) score from baseline to 6 weeks using a linear mixed-effect model that used data from all timepoints (6 weeks, 3, 6, 12 months). Results: 2212 participants were randomized. Six were excluded from analyses as ineligible. Of the 2116 eligible randomized participants (mean age 37 years, 80% women), 70.1% (1484/2116) had follow-up data available for analysis, and 56.9% (1205/2116) had data on the primary outcome, although attrition was higher in the intervention arm. At 6 weeks the mean (95% CI, P value) adjusted difference in change in SPIN-17 score in the intervention group compared to control, was -1.94 (-3.13 to -0.75, P=0.0014), a standardised mean difference effect size of 0.2. The improvement was maintained at 12 months. Given the high drop-out, sensitivity analyses explored missing data assumptions and were consistent with the primary analysis finding. The economic evaluation demonstrated cost-effectiveness with a small health status benefit and a reduction in health service utilisation. Conclusions: For people with social anxiety symptoms who are not receiving other forms of help, this study suggests that an online self-help tool based on cognitive behavioural principles can provide a small improvement in social anxiety symptoms compared with no intervention, although drop-out rates were high. Clinical Trial: ClinicalTrials.gov NCT02451878. https://clinicaltrials.gov/ct2/show/NCT0245187