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Register a new userLower Bounds on the Exchange-Correlation Energy in Reduced Dimensions
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Esa R\\\"as\\\"anen
Publication date
2009
fields
Physics
and research's language is
English
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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.
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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.
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.
We study a generic model of a Chern insulator supplemented by a Hubbard interaction in arbitrary even dimension $D$ and demonstrate that the model remains well-defined and nontrivial in the $D to infty$ limit. Dynamical mean-field theory is applicable and predicts a phase diagram with a continuum of topologically different phases separating a correlated Mott insulator from the trivial band insulator. We discuss various features, such as the elusive distinction between insulating and semi-metal states, which are unconventional already in the non-interacting case. Topological phases are characterized by a non-quantized Chern density replacing the Chern number as $Dto infty$.
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.
In this study, we investigate the isolated magnetic interactions between two identical Fe atoms divacantly-substituted into graphene. Using density functional theory, we simulated the electronic and magnetic properties for a supercell of graphene with spatial variation of the Fe atoms along either the armchair or zig-zag directions. Overall, we find that the exchange interaction between the two Fe atoms fluctuates from ferromagnetic to antiferromagnetic as a function of the spatial distance in the armchair direction. Given the induced magnetic moment and increased density of states at the Fermi level by the surrounding carbon atoms, we conclude that an RKKY-like interaction may characterize the exchange interactions between the Fe atoms. Furthermore, we examined the same interactions for Fe atoms along the zig-zag direction in graphene and found no evidence for an RKKY interaction as this system shows standard superexchange between the transition-metal impurities. Therefore, we determine that Fe-substituted graphene produces a directional-dependent spin interaction, which may provide stability to spintronic and multifunctional devices and applications for graphene.
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