Spin Hamiltonian of Hyperkagome Na4Ir3O8

We derive the spin Hamiltonian for the quantum spin liquid Na4Ir3O8, and then estimate the direct and superexchange contributions between near neighbor iridium ions using a tight binding parametrization of the electronic structure. We find a magnitude of the exchange interaction comparable to experiment for a reasonable value of the on-site Coulomb repulsion. For one of the two tight binding parametrizations we have studied, the direct exchange term, which is isotropic, dominates the total exchange. This provides support for those theories proposed to describe this novel quantum spin liquid that assume an isotropic Heisenberg model.Comment: 9 pages, 4 figure

Electronic Structure of Hyperkagome Na4Ir3O8

We investigate the electronic structure of the frustrated magnet Na4Ir3O8 using density functional theory. Due to strong spin-orbit coupling, the hyperkagome lattice is characterized by a half-filled complex of states, making it a cubic iridium analogue of the high temperature superconducting cuprates. The implications of our results for this unique material are discussed.Comment: expanded discussion with extra figures - 6 pages, 10 figure

The COVID-19 Threat : An Opportunity to Rethink the European Economic Constitution and European Private Law

Peer reviewe

Overview of cases before the CJEU on European Consumer Contract Law (2008–2013) – Part II

During the last five years the CJEU had to decide on more than 50 preliminary references in the area of consumer contract law. As a consequence there are far more than 100 decisions available which represent the increasingly concrete basis for a European contract law. Particularly striking is the rising number of questions referred to the CJEU by the new Member States. With regard to quantity, two fields stand out: legal conflicts about financial services of all kinds and about passenger rights. Since the CJEU has developed independent dogmatics for some areas of contract law, it might be necessary to rethink legal categories on the national level.Durant les cinq dernières années, la CJUE a dû répondre à plus de 50 questions préjudicielles dans le domaine du droit des contrats de consommation. En conséquence, il y a bien plus de 100 décisions disponibles qui représentent une base concrète croissante pour un droit européen des contrats. L’accroissement du nombre de questions adressées à la CJUE par les nouveaux Etats membres est particulièrement frappant. Quantitativement, deux domaines se distinguent : les conflits juridiques relatifs aux services financiers de toutes sortes et ceux relatifs auxprétations propres dans quelques domaines du droit des contrats, il pourrait être nécessaire de repenser les catégories juridiques au niveau national.In den letzten fünf Jahren hatte der EuGH mehr als 50 Vorlageverfahren zu entscheiden. Per dato liegen damit weit mehr als 100 Entscheidungen vor, die in immer dichterer Form die Grundlagen für ein europäisches Vertragsrecht konkretisieren. Auffällig ist die steigende Zahl von Vorlagen aus den neuen Mitgliedstaaten. In der Sache dominieren in quantitativer Hinsicht zwei Bereiche: rechtliche Auseinandersetzungen um Finanzdienstleistungen jedweder Art und das Passagier- bzw. Reiserecht. Für Teilbereiche des Vertragsrechts entwickelt der EuGH eine eigenständige Dogmatik, die ein Überdenken nationaler rechtlicher Kategorien notwendig macht

A topological classification of interaction-driven spin pumps

When adiabatically varied in time, certain one-dimensional band insulators allow for the quantized noiseless pumping of spin even in the presence of strong spin orbit scattering. These spin pumps are closely related to the quantum spin Hall system, and their properties are protected by a time-reversal restriction on the pumping cycle. In this paper we study pumps formed of one-dimensional insulators with a time-reversal restriction on the pumping cycle and a bulk energy gap which arises due to interactions. We find that the correlated gapped phase can lead to novel pumping properties. In particular, systems with $d$ different ground states can give rise to $d+1$ different classes of spin pumps, including a trivial class which does not pump quantized spin and $d$ non-trivial classes allowing for the pumping of quantized spin $\hbar/n$ on average per cycle, where $1\leq n\leq d$. We discuss an example of a spin pump that transfers on average spin $\hbar/2$ without transferring charge.Comment: 5 pages, 2 figure

New Private Law Theory—A Very Brief Introduction

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