Linearized Coupled Cluster Correction on the Antisymmetric Product of 1 reference orbital Geminals

We present a Linearized Coupled Cluster (LCC) correction based on an Antisymmetric Product of 1 reference orbital Geminals (AP1roG) reference state. In our LCC ansatz, the cluster operator is restricted to double and to single and double excitations as in standard single-reference CC theory. The performance of the AP1roG-LCC models is tested for the dissociation of diatomic molecules (C$_2$ and F$_2$), spectroscopic constants of the uranyl cation (UO$_2^{2+}$), and the symmetric dissociation of the H$_{50}$ hydrogen chain. Our study indicates that an LCC correction based on an AP1roG reference function is more robust and reliable than corrections based on perturbation theory, yielding spectroscopic constants that are in very good agreement with theoretical reference data.Comment: 9 pages, 4 figure

A matroid associated with a phylogenetic tree

A (pseudo-)metric D on a finite set X is said to be a `tree metric' if there is a finite tree with leaf set X and non-negative edge weights so that, for all x,y ∈X, D(x,y) is the path distance in the tree between x and y. It is well known that not every metric is a tree metric. However, when some such tree exists, one can always find one whose interior edges have strictly positive edge weights and that has no vertices of degree 2, any such tree is 13; up to canonical isomorphism 13; uniquely determined by D, and one does not even need all of the distances in order to fully (re-)construct the tree's edge weights in this case. Thus, it seems of some interest to investigate which subsets of X, 2 suffice to determine (`lasso') these edge weights. In this paper, we use the results of a previous paper to discuss the structure of a matroid that can be associated with an (unweighted) X-tree T defined by the requirement that its bases are exactly the `tight edge-weight lassos' for T, i.e, the minimal subsets of X, 2 that lasso the edge weights of T

Single magnetic adsorbates on s-wave superconductors

In superconductors, magnetic impurities induce a pair-breaking potential for Cooper pairs, which locally affects the Bogoliubov quasiparticles and gives rise to Yu-Shiba-Rusinov (YSR or Shiba, in short) bound states in the density of states (DoS). These states carry information on the magnetic coupling strength of the impurity with the superconductor, which determines the many-body ground state properties of the system. Recently, the interest in Shiba physics was boosted by the prediction of topological superconductivity and Majorana modes in magnetically coupled chains and arrays of Shiba impurities. Here, we review the physical insights obtained by scanning tunneling microscopy into single magnetic adsorbates on the $s$-wave superconductor lead (Pb). We explore the tunneling processes into Shiba states, show how magnetic anisotropy affects many-body excitations, and determine the crossing of the many-body groundstate through a quantum phase transition. Finally, we discuss the coupling of impurities into dimers and chains and their relation to Majorana physics.Comment: 18 pages, 17 figures, revie

Tuning the magnetic anisotropy of single molecules

The magnetism of single atoms and molecules is governed by the atomic scale environment. In general, the reduced symmetry of the surrounding splits the $d$ states and aligns the magnetic moment along certain favorable directions. Here, we show that we can reversibly modify the magnetocrystalline anisotropy by manipulating the environment of single iron(II) porphyrin molecules adsorbed on Pb(111) with the tip of a scanning tunneling microscope. When we decrease the tip--molecule distance, we first observe a small increase followed by an exponential decrease of the axial anisotropy on the molecules. This is in contrast to the monotonous increase observed earlier for the same molecule with an additional axial Cl ligand. We ascribe the changes in the anisotropy of both species to a deformation of the molecules in the presence of the attractive force of the tip, which leads to a change in the $d$ level alignment. These experiments demonstrate the feasibility of a precise tuning of the magnetic anisotropy of an individual molecule by mechanical control.Comment: 16 pages, 5 figures; online at Nano Letters (2015

Visualizing intramolecular distortions as the origin of transverse magnetic anisotropy

The magnetic properties of metal–organic complexes are strongly influenced by conformational changes in the ligand. The flexibility of Fe-tetra-pyridyl-porphyrin molecules leads to different adsorption configurations on a Au(111) surface. By combining low-temperature scanning tunneling spectroscopy and atomic force microscopy, we resolve a correlation of the molecular configuration with different spin states and magnitudes of magnetic anisotropy. When the macrocycle exhibits a laterally undistorted saddle shape, the molecules lie in a S = 1 state with axial anisotropy arising from a square-planar ligand field. If the symmetry in the molecular ligand field is reduced by a lateral distortion of the molecule, we find a finite contribution of transverse anisotropy. Some of the distorted molecules lie in a S = 2 state, again exhibiting substantial transverse anisotropy

Magnetic anisotropy in Shiba bound states across a quantum phase transition

The exchange coupling between magnetic adsorbates and a superconducting substrate leads to Shiba states inside the superconducting energy gap and a Kondo resonance outside the gap. The exchange coupling strength determines whether the quantum many-body ground state is a Kondo singlet or a singlet of the paired superconducting quasiparticles. Here, we use scanning tunneling spectroscopy to identify the different quantum ground states of Manganese phthalocyanine on Pb(111). We observe Shiba states, which are split into triplets by magnetocrystalline anisotropy. Their characteristic spectral weight yields an unambiguous proof of the nature of the quantum ground state.Comment: 6 pages, 4 figure

Regional and Transregional Currents in the Shallows of Lake Chad

Der Beitrag analysiert die Spannung zwischen der Interpretation eines Konflikts und den regionalen oder transregionalen Reaktionen darauf. Den empirischen Fokus bildet das militärische Vorgehen der Multinational Joint Task Force (MNJTF) – Benin, Kamerun, Tschad, Niger und Nigeria – gegen Boko Haram. Dieses Vorgehen ist zwar in einem regionalen Kontext verankert und wird von der Lake Chad Basin Commission (LCBC) koordiniert, doch zugleich auch in einem transregionalen Kontext, im Rahmen der Kooperation zwischen zwei Regional Economic Communities, der Economic Community of West African States (ECOWAS) und der Economic Community of Central African States (ECCAS). Keine dieser beiden räumlichen Verankerungen sind einfach gegeben, vielmehr sind es bestimmte Akteure, die den regionalen oder transregionalen Charakter des Konflikts und der entsprechenden Reaktionen produzieren und reproduzieren.This article addresses the tension between the conception of a conflict and the ensuing response as regional or as transregional. The empirical focus is the military response within the Multinational Joint Task Force (MNJTF) – comprised of Benin, Cameroon, Chad, Niger and Nigeria – against Boko Haram. This response is situated in a regional context, as its coordinating forum is the Lake Chad Basin Commission (LCBC), but also in a transregional one, through the cooperation between two Regional Economic Communities (RECs), the Economic Community of West African States (ECOWAS) and the Economic Community of Central African States (ECCAS). This article cautions that neither of these two framings is a given. Rather, particular actors produce and reproduce the regional or respectively transregional character of a security concern as well as its response