Search results for "Approx"
showing 10 items of 922 documents
Parameter-free density functional for the correlation energy in two dimensions
2010
Accurate treatment of the electronic correlation in inhomogeneous electronic systems, combined with the ability to capture the correlation energy of the homogeneous electron gas, allows to reach high predictive power in the application of density-functional theory. For two-dimensional systems we can achieve this goal by generalizing our previous approximation [Phys. Rev. B 79, 085316 (2009)] to a parameter-free form, which reproduces the correlation energy of the homogeneous gas while preserving the ability to deal with inhomogeneous systems. The resulting functional is shown to be very accurate for finite systems with an arbitrary number of electrons with respect to numerically exact refer…
Limits of lateral expansion in two-dimensional materials with line defects
2021
The flexibility of two-dimensional (2D) materials enables static and dynamic ripples that are known to cause lateral contraction, shrinking of the material boundary. However, the limits of 2D materials' \emph{lateral expansion} are unknown. Therefore, here we discuss the limits of intrinsic lateral expansion of 2D materials that are modified by compressive line defects. Using thin sheet elasticity theory and sequential multiscale modeling, we find that the lateral expansion is inevitably limited by the onset of rippling. The maximum lateral expansion $\chi_{max}\approx 2.1\cdot t^2\sigma_d$, governed by the elastic thickness $t$ and the defect density $\sigma_d$, remains typically well belo…
Magnetism in one-dimensional quantum dot arrays
2005
We employ the density functional Kohn-Sham method in the local spin-density approximation to study the electronic structure and magnetism of quasi one-dimensional periodic arrays of few-electron quantum dots. At small values of the lattice constant, the single dots overlap, forming a non-magnetic quantum wire with nearly homogenous density. As the confinement perpendicular to the wire is increased, i.e. as the wire is squeezed to become more one-dimensional, it undergoes a spin-Peierls transition. Magnetism sets in as the quantum dots are placed further apart. It is determined by the electronic shell filling of the individual quantum dots. At larger values of the lattice constant, the band …
Laplacian-level density functionals for the exchange-correlation energy of low-dimensional nanostructures
2010
In modeling low-dimensional electronic nanostructures, the evaluation of the electron-electron interaction is a challenging task. Here we present an accurate and practical density-functional approach to the two-dimensional many-electron problem. In particular, we show that spin-density functionals in the class of meta-generalized-gradient approximations can be greatly simplified by reducing the explicit dependence on the Kohn-Sham orbitals to the dependence on the electron spin density and its spatial derivatives. Tests on various quantum-dot systems show that the overall accuracy is well preserved, if not even improved, by the modifications.
Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model
2011
We study time-dependent electron transport through an Anderson model. The electronic interactions on the impurity site are included via the self-energy approximations at Hartree-Fock (HF), second Born (2B), GW, and T-matrix levels as well as within a time-dependent density functional (TDDFT) scheme based on the adiabatic Bethe-ansatz local density approximation (ABALDA) for the exchange-correlation potential. The Anderson model is driven out of equilibrium by applying a bias to the leads, and its nonequilibrium dynamics is determined by real-time propagation. The time-dependent currents and densities are compared to benchmark results obtained with the time-dependent density matrix renormali…
Quantum Monte Carlo simulations of antiferromagnetism in ultracold fermions on optical lattices within real-space dynamical mean-field theory
2010
We present a massively parallel quantum Monte Carlo based implementation of real-space dynamical mean-field theory for general inhomogeneous correlated fermionic lattice systems. As a first application, we study magnetic order in a binary mixture of repulsively interacting fermionic atoms harmonically trapped in an optical lattice. We explore temperature effects and establish signatures of the N\'{e}el transition in observables directly accessible in cold-atom experiments; entropy estimates are also provided. We demonstrate that the local density approximation (LDA) fails for ordered phases. In contrast, a "slab" approximation allows us to reach experimental system sizes with O(10^5) atoms …
Band Tails in a Disordered System
1993
In crystalline solids electronic excitations have a band structure. Energy intervals, in which excitations occur, are separated by band gaps, where the density of electronic states vanishes. At the band edge the density-of-states (DOS) has power law singularities, so-called van Hove singularities.
Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"
1998
We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the anal…
One dimensional arrays and solitary tunnel junctions in the weak coulomb blockade regime: CBT thermometry
1997
In this article we review the use of the tunnel junction arrays for primary thermometry. In addition to our basic experimental and theoretical results we stress the insensitivity of this method to the fluctuating background charges, to nonidealities in the array and to magnetic field. Important new results of this article are the low temperature corrections to the half width and depth of the measured conductance dip beyond the linear approximation. We also point ou that short arrays, single tunnel junctions in particular, show interesting deviations from the universal behaviour of the long arrays.
Transitions between metastable states in silica clusters
1999
Relaxation phenomena in glasses can be related to jump processes between different minima of the potential energy in the configuration space. These transitions play a key role in the low temperature regime, giving rise to tunneling systems responsible for the anomalous specific heat and thermal conductivity in disordered solids with respect to crystals. By using a recently developed numerical algorithm, we study the potential energy landscape of silica clusters, taking as a starting point the location of first order saddle points. This allows us to find a great number of adjacent minima. We analyze the degree of cooperativity of these transitions and the connection of physical properties wi…