Introduction: Principles and Practices of EU External Representation.

With this working paper, CLEER aims to offer a better insight into selected legal aspects concerning the European Union’s redefined diplomatic persona. In particular, the working paper will address issues pertaining to the Lisbon Treaty’s organising principles of EU external action, both under EU law and international law, and the growing practice of external representation of the European Union, especially in the context of other international organisations and bodies. Many questions remain unanswered in this respect, for instance: how can we best understand the relationship between the way the EU decides upon international positions and organises its external representation on the one hand, and its influence, performance and/or effectiveness on the other hand? Does the European Union’s formal status as a subject of international law justify an upgraded observer status within international organisations, a seat additional to that of the EU Member States, or should the EU replace them? Does it matter who speaks for the EU, and in what way? How should we square the emergence of the European External Action Service (EEAS), a hybrid organ consisting of EU civil servants and seconded diplomats from the Member States, with the traditionally state-centred body of international diplomatic law? And what can be expected from the High Representative, the EEAS and its vast network of diplomatic representations in third countries and multilateral settings in the pursuit of the Treaty’s external objectives

Magnetocaloric effect in quantum spin-s chains

We compute the entropy of antiferromagnetic quantum spin-s chains in an external magnetic field using exact diagonalization and Quantum Monte Carlo simulations. The magnetocaloric effect, i.e., temperature variations during adiabatic field changes, can be derived from the isentropes. First, we focus on the example of the spin-s=1 chain and show that one can cool by closing the Haldane gap with a magnetic field. We then move to quantum spin-s chains and demonstrate linear scaling with $s$ close to the saturation field. In passing, we propose a new method to compute many low-lying excited states using the Lanczos recursion.Comment: 11 pages including 6 figures, to appear in Condensed Matter Physics (Lviv

Classical and quantum two-dimensional anisotropic Heisenberg antiferromagnets

The classical and the quantum, spin $S=1/2, versions of the uniaxially anisotropic Heisenberg antiferromagnet on a square lattice in a field parallel to the easy axis are studied using Monte Carlo techniques. For the classical version, attention is drawn to biconical structures and fluctuations at low temperatures in the transition region between the antiferromagnetic and spin-flop phases. For the quantum version, the previously proposed scenario of a first-order transition between the antiferromagnetic and spin-flop phases with a critical endpoint and a tricritical point is scrutinized.Comment: 5 pages, 7 figures, accepted by Phys. Rev.

Non-local updates for quantum Monte Carlo simulations

We review the development of update schemes for quantum lattice models simulated using world line quantum Monte Carlo algorithms. Starting from the Suzuki-Trotter mapping we discuss limitations of local update algorithms and highlight the main developments beyond Metropolis-style local updates: the development of cluster algorithms, their generalization to continuous time, the worm and directed-loop algorithms and finally a generalization of the flat histogram method of Wang and Landau to quantum systems.Comment: 14 pages, article for the proceedings of the "The Monte Carlo Method in the Physical Sciences: Celebrating the 50th Anniversary of the Metropolis Algorithm", Los Alamos, June 9-11, 200

Nonordinary edge criticaliy of two-dimensional quantum critical magnets

Based on large-scale quantum Monte Carlo simulations, we examine the correlations along the edges of two-dimensional semi-infinite quantum critical Heisenberg spin-$1/2$ systems. In particular, we consider coupled quantum spin-dimer systems at their bulk quantum critical points, including the columnar-dimer model and the plaquette-square lattice. The alignment of the edge spins strongly affects these correlations and the corresponding scaling exponents, with remarkably similar values obtained for various quantum spin-dimer systems. We furthermore observe subtle effects on the scaling behavior from perturbing the edge spins that exhibit the genuine quantum nature of these edge states. Our observations furthermore challenge recent attempts that relate the edge spin criticality to the presence of symmetry-protected topological phases in such quantum spin systems.Comment: 9 pages, 11 figures, v2: as publishe

Persistent supersolid phase of hard-core bosons on the triangular lattice

We study hard-core bosons with unfrustrated hopping ($t$) and nearest neighbour repulsion ($U$) on the triangular lattice. At half-filling, the system undergoes a zero temperature ($T$) quantum phase transition from a superfluid phase at small $U$ to a supersolid at $U_c \approx 4.45$ in units of $2t$. This supersolid phase breaks the lattice translation symmetry in a characteristic $\sqrt{3} \times \sqrt{3}$ pattern, and is remarkably stable--indeed, a smooth extrapolation of our results indicates that the supersolid phase persists for arbitrarily large $U/t$.Comment: 4 pages, 5 figures, two column forma

Supersolids in confined fermions on one-dimensional optical lattices

Using quantum Monte Carlo simulations, we show that density-density and pairing correlation functions of the one-dimensional attractive fermionic Hubbard model in a harmonic confinement potential are characterized by the anomalous dimension $K_\rho$ of a corresponding periodic system, and hence display quantum critical behavior. The corresponding fluctuations render the SU(2) symmetry breaking by the confining potential irrelevant, leading to structure form factors for both correlation functions that scale with the same exponent upon increasing the system size, thus giving rise to a (quasi)supersolid.Comment: 4 pages, 5 figures, published versio

Dynamical Mean Field Theory for the Bose-Hubbard Model

The dynamical mean field theory (DMFT), which is successful in the study of strongly correlated fermions, was recently extended to boson systems [Phys. Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT to study the Bose-Hubbard model which describes on-site interacting bosons in a lattice. Using exact diagonalization as the impurity solver, we get the DMFT solutions for the Green's function, the occupation density, as well as the condensate fraction on a Bethe lattice. Various phases are identified: the Mott insulator, the Bose-Einstein condensed (BEC) phase, and the normal phase. At finite temperatures, we obtain the crossover between the Mott-like regime and the normal phase, as well as the BEC-to-normal phase transition. Phase diagrams on the $\mu/U-\tilde{t}/U$ plane and on the $T/U-\tilde{t}/U$ plane are produced ($\tilde{t}$ is the scaled hopping amplitude). We compare our results with the previous ones, and discuss the implication of these results to experiments.Comment: 11 pages, 8 figure