arXiv subjects

R. W. Godby

Publications and source records attributed to R. W. Godby.

At least 37 records · Page 2Linked to original sources

arXiv2007

Vertex corrections in localized and extended systems

Within many-body perturbation theory we apply vertex corrections to various closed-shell atoms and to jellium, using a local approximation for the vertex consistent with starting the many-body perturbation theory from a DFT-LDA Green's function. The vertex appears in two places -- in the screened Coulomb interaction, W, and in the self-energy, Σ-- and we obtain a systematic discrimination of these two effects by turning the vertex in Σon and off. We also make comparisons to standard GW results within the usual random-phase approximation (RPA), which omits the vertex from both. When a vertex is included for closed-shell atoms, both ground-state and excited-state properties demonstrate only limited improvements over standard GW. For jellium we observe marked improvement in the quasiparticle band width when the vertex is included only in W, whereas turning on the vertex in Σleads to an unphysical quasiparticle dispersion and work function. A simple analysis suggests why implementation of the vertex only in W is a valid way to improve quasiparticle energy calculations, while the vertex in Σis unphysical, and points the way to development of improved vertices for ab initio electronic structure calculations.

cond-mat.mtrl-sci↗

arXiv2007

Treatment of electron viscosity in quantum conductance

In a recent paper Sai {\it et al.} [1] identified a correction $R^{dyn}$ to the DC conductance of nanoscale junctions arising from dynamical exchange-correlation ($XC$) effects within time-dependent density functional theory. This quantity contributes to the total resistance through $R=R_{s}+R^{dyn}$ where $R_{s}$ is the resistance evaluated in the absence of dynamical $XC$ effects. In this Comment we show that the numerical estimation of $R^{dyn}$ in example systems of the type they considered should be considerably reduced, once a more appropriate form for the shear electron viscosity $η$ is used.

cond-mat.mtrl-sci↗

arXiv2007

Self-interaction in Green's-function theory of the hydrogen atom

Atomic hydrogen provides a unique test case for computational electronic structure methods, since its electronic excitation energies are known analytically. With only one electron, hydrogen contains no electronic correlation and is therefore particularly susceptible to spurious self-interaction errors introduced by certain computational methods. In this paper we focus on many-body perturbation-theory (MBPT) in Hedin's GW approximation. While the Hartree-Fock and the exact MBPT self-energy are free of self-interaction, the correlation part of the GW self-energy does not have this property. Here we use atomic hydrogen as a benchmark system for GW and show that the self-interaction part of the GW self-energy, while non-zero, is small. The effect of calculating the GW self-energy from exact wavefunctions and eigenvalues, as distinct from those from the local-density approximation, is also illuminating.

cond-mat.mtrl-sci↗

arXiv2006

Hartree-Fock Theory of a Current-Carrying Electron Gas

State-of-the-art simulation tools for non-equilibrium quantum transport systems typically take the current-carrier occupations to be described in terms of equilibrium distribution functions characterised by two different electro-chemical potentials, while for the description of electronic exchange and correlation, the local density approximation (LDA) to density functional theory (DFT) is generally used. However this involves an inconsistency because the LDA is based on the h omogeneous electron gas in equilibrium, while the system is not in equilibrium and may be far from it. In this paper we analyze this inconsistency by studying the interplay between non-equilibrium occupancies obtained from a maximum entropy approach and the Hartree-Fock exchange energy, single-particle spectrum and exchange hole, for the case of a two-dimensional homogeneous electron gas. The current-dependence of the local exchange potential is also discussed. It is found that the single-particle spectrum and exchange hole have a significant dependence on the current which has not been taken into account in practical calculations. The exchange energy and the local exchange potential, however, are shown to change very little with respect to their equilibrium counterparts. The weak dependence of these quantities on the current is explained in terms of the symmetries of the exchange hole.

cond-mat.mes-hall↗

arXiv2006

Dielectric anisotropy in the GW space-time method

Excited-state calculations, notably for quasiparticle band structures, are nowadays routinely performed within the GW approximation for the electronic self-energy. Nevertheless, certain numerical approximations and simplifications are still employed in practice to make the computations feasible. An important aspect for periodic systems is the proper treatment of the singularity of the screened Coulomb interaction in reciprocal space, which results from the slow 1/r decay in real space. This must be done without introducing artificial interactions between the quasiparticles and their periodic images in repeated cells, which occur when integrals of the screened Coulomb interaction are discretised in reciprocal space. An adequate treatment of both aspects is crucial for a numerically stable computation of the self-energy. In this article we build on existing schemes for isotropic screening and present an extension for anisotropic systems. We also show how the contributions to the dielectric function arising from the non-local part of the pseudopotentials can be computed efficiently. These improvements are crucial for obtaining a fast convergence with respect to the number of points used for the Brillouin zone integration and prove to be essential to make GW calculations for strongly anisotropic systems, such as slabs or multilayers, efficient.

cond-mat.mtrl-sci↗

arXiv2006

Quantum conductance of homogeneous and inhomogeneous interacting electron systems

We obtain the conductance of a system of electrons connected to leads, within time-dependent density-functional theory, using a direct relation between the conductance and the density response function. Corrections to the non-interacting conductance appear as a consequence of the functional form of the exchange-correlation kernel at small frequencies and wavevectors. The simple adiabatic local-density approximation and non-local density-terms in the kernel both give rise to significant corrections in general. In the homogeneous electron gas, the former correction remains significant, and leads to a failure of linear-response theory for densities below a critical value.

cond-mat.mtrl-sci↗

arXiv2005

Current-constraining variational approaches to quantum transport

Presently, the main methods for describing a non-equilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical non-equilibrium density operator from principles of statistical mechanics, in a spirit close to Gibbs ensembles for equilibrium systems, leading to a variational principle for the non-equilibrium steady state. We discuss the existing attempts to achieve this using the maximum entropy principle based on constraining the average current. We show that the current-constrained theories result in a zero induced drop in electrostatic potential, so that such ensembles cannot correspond to the time-evolved density matrix, unless left- and right-going scattering states are mutually incoherent.

cond-mat.mtrl-sci↗

arXiv2004

Image states in metal clusters

The existence of image states in small clusters is shown, using a quantum-mechanical many-body approach. We present image state energies and wave functions for spherical jellium clusters up to 186 atoms, calculated in the GW approximation, where G is the Green's function, and W the dynamically screened Coulomb interaction, which by construction contains the dynamic long-range correlation effects that give rise to image effects. In addition we find that image states are also subject to quantum confinement. To extrapolate our investigations to clusters in the mesoscopic size range, we propose a semiclassical model potential, which we test against our full GW results.

cond-mat.mtrl-sci↗

arXiv2004

Assessment of density functional approximations: long-range correlations and self-interaction effects

The complex nature of electron-electron correlations is made manifest in the very simple but non-trivial problem of two electrons confined within a sphere. The description of highly non-local correlation and self-interaction effects by widely used local and semi-local exchange-correlation energy density functionals is shown to be unsatisfactory in most cases. Even the best such functionals exhibit significant errors in the Kohn-Sham potentials and density profiles.

cond-mat.other↗

arXiv2004

Conductance and polarization in quantum junctions

We revisit the expression for the conductance of a general nanostructure -- such as a quantum point contact -- as obtained from the linear response theory. We show that the conductance represents the strength of the Drude singularity in the conductivity $σ(k,k';iω\to 0)$. Using the equation of continuity for electric charge we obtain a formula for conductance in terms of polarization of the system. This identification can be used for direct calculation of the conductance for systems of interest even at the {\it ab-initio} level. In particular, we show that one can evaluate the conductance from calculations for a finite system without the need for special ``transport'' boundary conditions.

cond-mat.mtrl-sci↗

arXiv2003

Image resonance in the many-body density of states at a metal surface

The electronic properties of a semi-infinite metal surface without a bulk gap are studied by a formalism able to account for the continuous spectrum of the system. The density of states at the surface is calculated within the $GW$ approximation of many-body perturbation theory. We demonstrate the presence of an unoccupied surface resonance peaked at the position of the first image state. The resonance encompasses the whole Rydberg series of image states and cannot be resolved into individual peaks. Its origin is the shift in spectral weight when many-body correlation effects are taken into account.

cond-mat.mtrl-sci↗

arXiv2003

Maximum-entropy theory of steady-state quantum transport

We develop a new theoretical framework for describing steady-state quantum transport phenomena, based on the general maximum-entropy principle of non-equilibrium statistical mechanics. The general form of the many-body density matrix is derived, which contains the invariant part of the current operator that guarantees the non-equilibrium and steady-state character of the ensemble. Several examples of the theory are given, demonstrating the relationship of the present treatment to the widely-used scattering-states occupation schemes at the level of the self-consistent single-particle approximation.

cond-mat.mes-hall↗

arXiv2001

Many-body GW Calculations of Ground-State Properties: Quasi-2D Electron Systems and van der Waals Forces

We present GW many-body results for ground-state properties of two simple but very distinct families of inhomogenous systems in which traditional implementations of density-functional theory (DFT) fail drastically. The GW approach gives notably better results than the well-known random-phase approximation, at a similar computational cost. These results establish GW as a superior alternative to standard DFT schemes without the expensive numerical effort required by quantum Monte Carlo simulations.

cond-mat.mtrl-sci↗

arXiv2001

Diagrammatic self-energy approximations and the total particle number

There is increasing interest in many-body perturbation theory as a practical tool for the calculation of ground-state properties. As a consequence, unambiguous sum rules such as the conservation of particle number under the influence of the Coulomb interaction have acquired an importance that did not exist for calculations of excited-state properties. In this paper we obtain a rigorous, simple relation whose fulfilment guarantees particle-number conservation in a given diagrammatic self-energy approximation. Hedin's G_0W_0 approximation does not satisfy this relation and hence violates the particle-number sum rule. Very precise calculations for the homogeneous electron gas and a model inhomogeneous electron system allow the extent of the nonconservation to be estimated.

cond-mat.mtrl-sci↗

arXiv2000

Efficient Total Energy Calculations from Self-Energy Models

We propose a new method for calculating total energies of systems of interacting electrons, which requires little more computational resources than standard density-functional theories. The total energy is calculated within the framework of many-body perturbation theory by using an efficient model of the self-energy, that nevertheless retains the main features of the exact operator. The method shows promising performance when tested against quantum Monte Carlo results for the linear response of the homogeneous electron gas and structural properties of bulk silicon.

cond-mat↗

arXiv2000

Self-Consistent Calculation of Total Energies of the Electron Gas Using Many-Body Perturbation Theory

The performance of many-body perturbation theory for calculating ground-state properties is investigated. We present fully numerical results for the electron gas in three and two dimensions in the framework of the GW approximation. The overall agreement with very accurate Monte Carlo data is excellent, even for those ranges of densities for which the GW approach is often supposed to be unsuitable. The latter seems to be due to the fulfilment of general conservation rules. These results open further prospects for accurate calculations of ground-state properties circumventing the limitations of standard density functional theory.

cond-mat↗

arXiv1999

Enhancements to the GW space-time method

We describe the following new features which significantly enhance the power of the recently developed real-space imaginary-time GW scheme (Rieger et al., Comp. Phys. Commun. 117, 211 (1999)) for the calculation of self-energies and related quantities of solids: (i) to fit the smoothly decaying time/energy tails of the dynamically screened Coulomb interaction and other quantities to model functions, treating only the remaining time/energy region close to zero numerically and performing the Fourier transformation from time to energy and vice versa by a combination of analytic integration of the tails and Gauss-Legendre quadrature of the remaining part and (ii) to accelerate the convergence of the band sum in the calculation of the Green's function by replacing higher unoccupied eigenstates by free electron states (plane waves). These improvements make the calculation of larger systems (surfaces, clusters, defects etc.) accessible.

cond-mat↗

arXiv1998

The GW space-time method for the self-energy of large systems

We present a detailed account of the GW space-time method. The method increases the size of systems whose electronic structure can be studied with a computational implementation of Hedin's GW approximation. At the heart of the method is a representation of the Green's function G and the screened Coulomb interaction W in the real-space and imaginary-time domain, which allows a more efficient computation of the self-energy approximation Sigma = iGW. For intermediate steps we freely change between representations in real and reciprocal space on the one hand, and imaginary time and imaginary energy on the other, using fast Fourier transforms. The power of the method is demonstrated using the example of Si with artificially increased unit cell sizes.

cond-mat↗