arXiv subjects

Michael Seidl

Publications and source records attributed to Michael Seidl.

25 records · Page 2Linked to original sources

arXiv2009

Adiabatic connection at negative coupling strengths

The adiabatic connection of density functional theory (DFT) for electronic systems is generalized here to negative values of the coupling strength $α$ (with {\em attractive} electrons). In the extreme limit $α\to-\infty$ a simple physical solution is presented and its implications for DFT (as well as its limitations) are discussed. For two-electron systems (a case in which the present solution can be calculated exactly), we find that an interpolation between the limit $α\to-\infty$ and the opposite limit of infinitely strong repulsion ($α\to+\infty$) yields a rather accurate estimate of the second-order correlation energy $E\cor\glt[ρ]$ for several different densities $ρ$, without using virtual orbitals. The same procedure is also applied to the Be isoelectronic series, analyzing the effects of near-degeneracy.

cond-mat.other↗

arXiv2009

Density functional theory for strongly interacting electrons

We present an alternative to the Kohn-Sham formulation of density functional theory for the ground-state properties of strongly interacting electronic systems. The idea is to start from the limit of zero kinetic energy and systematically expand the universal energy functional of the density in powers of a "coupling constant" that controls the magnitude of the kinetic energy. The problem of minimizing the energy is reduced to the solution of a strictly correlated electron problem in the presence of an effective potential, which plays in our theory the same role that the Kohn-Sham potential plays in the traditional formulation. We discuss several schemes for approximating the energy functional, and report preliminary results for low-density quantum dots.

cond-mat.str-el↗

arXiv2008

Electronic zero-point oscillations in the strong-interaction limit of density functional theory

The exchange-correlation energy in Kohn-Sham density functional theory can be expressed exactly in terms of the change in the expectation of the electron-electron repulsion operator when, in the many-electron hamiltonian, this same operator is multiplied by a real parameter $λ$ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is kept fixed by a suitable local one-body potential. The strong-interaction limit of density functional theory, defined as the limit $λ\to\infty$, turns out to be, like the opposite non-interacting Kohn-Sham limit ($λ\to 0$) mathematically simpler than the physical ($λ=1$) case, and can be used to build an approximate interpolation formula between $λ\to 0$ and $λ\to\infty$ for the exchange-correlation energy. Here we extend the exact treatment of the $λ\to\infty$ limit [Phys. Rev. A {\bf 75}, 042511 (2007)] to the next leading term, describing zero-point oscillations of strictly correlated electrons, with numerical examples for small spherical atoms. We also propose an improved approximate functional for the zero-point term and a revised interpolation formula for the exchange-correlation energy satisfying more exact constraints.

cond-mat.str-el↗

arXiv2008

Intracule densities in the strong-interaction limit of density functional theory

The correlation energy in density functional theory can be expressed exactly in terms of the change in the probability of finding two electrons at a given distance $r_{12}$ (intracule density) when the electron-electron interaction is multiplied by a real parameter $λ$ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is (ideally) kept fixed by a suitable local one-body potential. While an accurate intracule density of the physical system can only be obtained from expensive wavefunction-based calculations, being able to construct good models starting from Kohn-Sham ingredients would highly improve the accuracy of density functional calculations. To this purpose, we investigate the intracule density in the $λ\to\infty$ limit of the adiabatic connection. This strong-interaction limit of density functional theory turns out to be, like the opposite non-interacting Kohn-Sham limit, mathematically simple and can be entirely constructed from the knowledge of the one-electron density. We develop here the theoretical framework and, using accurate correlated one-electron densities, we calculate the intracule densities in the strong interaction limit for few atoms. Comparison of our results with the corresponding Kohn-Sham and physical quantities provides useful hints for building approximate intracule densities along the adiabatic connection of density functional theory.

cond-mat.other↗

arXiv2007

The Fermionic Density-functional at Feshbach Resonance

We consider a dilute gas of neutral unpolarized fermionic atoms at zero temperature.The atoms interact via a short range (tunable) attractive interaction. We demonstrate analytically a curious property of the gas at unitarity. Namely, the correlation energy of the gas, evaluated by second order perturbation theory, has the same density dependence as the first order exchange energy, and the two almost exactly cancel each other at Feshbach resonance irrespective of the shape of the potential, provided $(μr_s) >> 1$. Here $(μ)^{-1}$ is the range of the two-body potential, and $r_s$ is defined through the number density $n=3/(4πr_s^3)$. The implications of this result for universality is discussed.

cond-mat.other↗

arXiv2007

Strictly correlated electrons in density functional theory: A general formulation with applications to spherical densities

We reformulate the strong-interaction limit of electronic density functional theory in terms of a classical problem with a degenerate minimum. This allows us to clarify many aspects of this limit, and to write a general solution, which is explicitly calculated for spherical densities. We then compare our results with previous approximate solutions and discuss the implications for density functional theory.

cond-mat.mtrl-sci↗

arXiv2003

Spin-resolved second-order correlation energy of the two-dimensional uniform electron gas

For the two-dimensional electron gas, the exact high-density limit of the correlation energy is evaluated here numerically for all values of the spin polarization. The result is spin-resolved into $\uparrow\uparrow$, $\uparrow\downarrow$, and $\downarrow\downarrow$ contributions and parametrized analytically. Interaction-strength interpolation yields a simple model (LSD) for the correlation energy at finite densities.

cond-mat.mtrl-sci↗