On the validity of power functionals for the homogeneous electron gas in reduced.density-matrix-functional theory

Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced density-matrix functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form $f(n,n')=(n n')^\alpha$ for the scaling function in the exchange-correlation energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power $\alpha$ to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlation energy and exclude pinned states with the condition $n({\mathbf k})<1$ for all wave vectors ${\mathbf k}$. The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for $\alpha$ that yield the exact correlation energy and its kinetic part for both the three- and two-dimensional electron gas. In both systems, narrow regimes of validity and accuracy are found at $\alpha\gtrsim 0.6$ and at $r_s\gtrsim 10$ for the density parameter, corresponding to relatively low densities.Comment: Phys. Rev. A (in print, 2016

Quest for a Phantom Investigating Abu l-Huda al-Sayyadi

Abu l-Huda was born in a small village on the margins of the northern Syrian desert in 1850 into a family of humble origins. In his early childhood, he was initiated into the Rifaciyya order, which is still widely spread today in the rural areas of Syria and Iraq. He was quick to develop substantial contacts with Rifaci sheiks in Aleppo, who dominated certain important posts in the city. In 1874, he became the naqib ala shraf (scion of the descendants of the prophets) there at a strikingly young age. In the following years, he managed to overcome several severe setbacks to his career and finally established himself in the entourage of the new Sultan Abdlhamid II, whose accession to the throne marked the end of the tanzimat, a period of wide-ranging administrative reforms in Ottoman history

Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas

We derive an intrinsically temperature-dependent approximation to the correlation grand potential for many-electron systems in thermodynamical equilibrium in the context of finite-temperature reduced-density-matrix-functional theory (FT-RDMFT). We demonstrate its accuracy by calculating the magnetic phase diagram of the homogeneous electron gas. We compare it to known limits from highly accurate quantum Monte Carlo calculations as well as to phase diagrams obtained within existing exchange-correlation approximations from density functional theory and zero-temperature RDMFT

Excited states in bilayer graphene quantum dots

We report on ground- and excited state transport through an electrostatically defined few-hole quantum dot in bilayer graphene in both parallel and perpendicular applied magnetic fields. A remarkably clear level scheme for the two-particle spectra is found by analyzing finite bias spectroscopy data within a two-particle model including spin and valley degrees of freedom. We identify the two-hole ground-state to be a spin-triplet and valley-singlet state. This spin alignment can be seen as Hund's rule for a valley-degenerate system, which is fundamentally different to quantum dots in carbon nano tubes and GaAs-based quantum dots. The spin-singlet excited states are found to be valley-triplet states by tilting the magnetic field with respect to the sample plane. We quantify the exchange energy to be 0.35meV and measure a valley and spin g-factor of 36 and 2, respectively