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Register a new userOn the lower bound on the exchange-correlation energy in two dimensions
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Added by
Esa R\\\"as\\\"anen
Publication date
2009
fields
Physics
and research's language is
English
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We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature.
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Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained, and give evidence of an interesting dimensional crossover between two and one dimensions.
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 reference data.
The competition between kinetic energy and Coulomb interactions in electronic systems can lead to complex many-body ground states with competing superconducting, charge density wave, and magnetic orders. Here we study the low temperature phases of a strongly interacting zinc-oxide-based high mobility two dimensional electron system that displays a tunable metal-insulator transition. Through a comprehensive analysis of the dependence of electronic transport on temperature, carrier density, in-plane and perpendicular magnetic fields, and voltage bias, we provide evidence for the existence of competing correlated metallic and insulating states with varying degrees of spin polarization. Our system features an unprecedented level of agreement with the state-of-the-art Quantum Monte Carlo phase diagram of the ideal jellium model, including a Wigner crystallization transition at a value of the interaction parameter $r_ssim 30$ and the absence of a pure Stoner transition. In-plane field dependence of transport reveals a new low temperature state with partial spin polarization separating the spin unpolarized metal and the Wigner crystal, which we examine against possible theoretical scenarios such as an anti-ferromagnetic crystal, Coulomb induced micro-emulsions, and disorder driven puddle formation.
Above the Kondo temperature, the Kohn-Sham zero-bias conductance of an Anderson junction has been shown to completely miss the Coulomb blockade. Within a standard model for the spectral function, we deduce a parameterization for both the onsite exchange-correlation potential and the bias drop as a function of the site occupation that applies for all correlation strengths. We use our results to sow doubt on the common interpretation of such corrections as arising from dynamical exchange-correlation contributions.
We report photoemission experiments revealing the valence electron spectral function of Mn, Fe, Co and Ni atoms on the Ag(100) surface. The series of spectra shows splittings of higher energy features which decrease with the filling of the 3d shell and a highly non-monotonous evolution of spectral weight near the Fermi edge. First principles calculations demonstrate that two manifestations of Hunds exchange $J$ are responsible for this evolution. First, there is a monotonous reduction of the effective exchange splittings with increasing filling of the 3d shell. Second, the amount of charge fluctuations and, thus, the weight of quasiparticle peaks at the Fermi level varies non-monotonously through this 3d series due to a distinct occupancy dependence of effective charging energies $U_{rm eff}$.
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