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We present a detailed study of the topological Schwinger model [Phys. Rev. D 99, 014503 (2019)2470-001010.1103/PhysRevD.99.014503], which describes (1+1) quantum electrodynamics of an Abelian U(1) gauge field coupled to a symmetry-protected topological matter sector, by means of a class of ZN lattice gauge theories. Employing density-matrix renormalization group techniques that exactly implement Gauss' law, we show that these models host a correlated topological phase for different values of N, where fermion correlations arise through interparticle interactions mediated by the gauge field. Moreover, by a careful finite-size scaling, we show that this phase is stable in the large-N limit and that the phase boundaries are in accordance with bosonization predictions of the U(1) topological Schwinger model. Our results demonstrate that ZN finite-dimensional gauge groups offer a practical route for an efficient classical simulation of equilibrium properties of electromagnetism with topological fermions. Additionally, we describe a scheme for the quantum simulation of a topological Schwinger model exploiting spin-changing collisions in boson-fermion mixtures of ultracold atoms in optical lattices. Although technically challenging, this quantum simulation would provide an alternative to classical density-matrix renormalization group techniques, providing also an efficient route to explore real-time nonequilibrium phenomena.

We study the out-of-equilibrium properties of 1 + 1 dimensional quantum electrodynamics (QED), discretized via the staggered-fermion Schwinger model with an Abelian Z(n) gauge group. We look at two relevant phenomena: first, we analyze the stability of the Dirac vacuum with respect to particle/antiparticle pair production, both spontaneous and induced by an external electric field; then, we examine the string breaking mechanism. We observe a strong effect of confinement, which acts by suppressing both spontaneous pair production and string breaking into quark/antiquark pairs, indicating that the system dynamics displays a number of out-of-equilibrium features.

Although even before the end of World War II the world was preparing itself to fight a relapse into stagnation, the harrowing role inflation was to have as a constant in the post-war economic scene was scarcely perceived. This resulted in several countries’ policy makers being caught off guard, with inflation proving to be a most intractable problem. The present article argues for a shift in emphasis in economic policy from monetary and fiscal issues towards growth, its determinants and its relationship to anti-inflation policies. The evolution of thinking on the problem of inflation is first considered. Employment and growth are then analysed in relation to inflation and economic policy. The author points out that full-employment and growth are neither synonymous nor interchangeable. JEL: E31, E24, E52, E62, Moneta e Credito, V. 29, N. 116 (1976)

Tutte le monete sono unità di conto. Tutte svolgono la funzione cosi detta di “ metro di valore”, ma non tutte con ugual efficienza. Le differenze sono registrate, nel lungo periodo, da variazioni del tasso di cambio. Se comprendiamo tutto intero il periodo che va dalle riforme monetarie post-belliche ai giorni nostri, nessuna moneta può vantarsi di essere rimasta in senso assoluto un buon metro di valore., Moneta e Credito, V. 29, N. 113 (1976)

The first official endeavours to bring about European monetary union were made when the system of fixed exchange rates was on the verge of collapse; in the intervening years the situation has hardly been more favourable than at the outset. Recently, however, things have started to look up again. While the dangers with which the world economic outlook is fraught point, no less clearly than in the past, to the crucial role of monetary unification for the survival of the Community, the difficulties which stand in the way of unification now seem to be less forbidding. The present paper draws attention to developments in the world economy and in EEC member countries that seem to justify this. In addition, some specific steps are suggested that would advance monetary unification. JEL: F36, F31, E43, Moneta e Credito, V. 31, N. 121 (1978)

The first official endeavours to bring about European monetary union were made when the system of fixed exchange rates was on the verge of collapse; in the intervening years the situation has hardly been more favourable than at the outset. Recently, however, things have started to look up again. While the dangers with which the world economic outlook is fraught point, no less clearly than in the past, to the crucial role of monetary unification for the survival of the Community, the difficulties which stand in the way of unification now seem to be less forbidding. The present paper draws attention to developments in the world economy and in EEC member countries that seem to justify this. In addition, some specific steps are suggested that would advance monetary unification. JEL: F36, F31, E43, PSL Quarterly Review, V. 31, N. 124 (1978)

Although even before the end of World War II the world was preparing itself to fight a relapse into stagnation, the harrowing role inflation was to have as a constant in the post-war economic scene was scarcely perceived. This resulted in several countries’ policy makers being caught off guard, with inflation proving to be a most intractable problem. The present article argues for a shift in emphasis in economic policy from monetary and fiscal issues towards growth, its determinants and its relationship to anti-inflation policies. The evolution of thinking on the problem of inflation is first considered. Employment and growth are then analysed in relation to inflation and economic policy. The author points out that full-employment and growth are neither synonymous nor interchangeable. JEL: E31, E24, E52, E62, PSL Quarterly Review, V. 29, N. 119 (1976)

Many argue that the crisis of the international monetary order founded at Bretton Woods is acting as a catalyst in the process of European monetary unification. Others, however, argue that the mounting disorder into which the Bretton Woods order has drifted is hampering that process and that, sooner or later, it will wreck the whole E.C. construction. The present article assess the international currency problem with regards to European integration, showing that it is probable that each of the arguments put forth have valid points. The author argues that the frictions produced by the process of reform have put a strain on international economic and monetary cooperation just when it needed to be strengthened in order to meet new challenges. Moreover, the repeated efforts to restore the monocentric reserve-currency system and the all round obligation to maintain fixed exchange rages are misdirected endeavours. JEL: E42, F36, F33, PSL Quarterly Review, V. 26, N. 107 (1973)

8 pages, 2 figures, Research Infrastructures (RIs) are large-scale facilities encompassing instruments, resources, data and services used by the scientific community to conduct high-level research in their respective fields. The development and integration of marine environmental RIs as European Research Vessel Operators [ERVO] (2020) is the response of the European Commission (EC) to global marine challenges through research, technological development and innovation. These infrastructures (EMSO ERIC, Euro-Argo ERIC, ICOS-ERIC Marine, LifeWatch ERIC, and EMBRC-ERIC) include specialized vessels, fixed-point monitoring systems, Lagrangian floats, test facilities, genomics observatories, bio-sensing, and Virtual Research Environments (VREs), among others. Marine ecosystems are vital for life on Earth. Global climate change is progressing rapidly, and geo-hazards, such as earthquakes, volcanic eruptions, and tsunamis, cause large losses of human life and have massive worldwide socio-economic impacts. Enhancing our marine environmental monitoring and prediction capabilities will increase our ability to respond adequately to major challenges and efficiently. Collaboration among European marine RIs aligns with and has contributed to the OceanObs’19 Conference statement and the objectives of the UN Decade of Ocean Science for Sustainable Development (2021–2030). This collaboration actively participates and supports concrete actions to increase the quality and quantity of more integrated and sustained observations in the ocean worldwide. From an innovation perspective, the next decade will increasingly count on marine RIs to support the development of new technologies and their validation in the field, increasing market uptake and produce a shift in observing capabilities and strategies, Parts of this paper have been supported by EU projects EMSODEV contract 676555 (see EMSODEV, 2020), and EMSO-Link contract 731036

The interplay of symmetry, topology, and many-body effects in the classification of possible phases of matter poses a formidable challenge that is attracting great attention in condensed-matter physics. Such many-body effects are typically induced by inter-particle interactions involving an action at a distance, such as the Coulomb interaction between electrons in a symmetry-protected topological (SPT) phase. In this work, we show that similar phenomena also appear in high-energy physics, where inter-particle interactions are mediated by gauge bosons, and constrained by a local gauge symmetry. We introduce a variant of the so-called Schwinger model, which describes quantum electrodynamics in (1+1) dimensions (QED$_2$), and show that it can host SPT phases with a topological contribution to the vacuum {\theta} angle, which leads to a new type of topological QED$_2.$ We use bosonization and density-matrix renormalization group techniques to study its rich phase diagram in great detail, and present a scheme for its realization in experiments of ultra-cold atoms in optical lattices., Comment: closer to published version

We investigate a model of hard-core bosons with infinitely repulsive nearest- and next-nearest-neighbor interactions in one dimension, introduced by Fendley, Sengupta and Sachdev in Phys. Rev. B 69, 075106 (2004). Using a combination of exact diagonalization, tensor network, and quantum Monte Carlo simulations, we show how an intermediate incommensurate phase separates a crystalline and a disordered phase. We base our analysis on a variety of diagnostics, including entanglement measures, fidelity susceptibility, correlation functions, and spectral properties. According to theoretical expectations, the disordered-to-incommensurate-phase transition point is compatible with Berezinskii-Kosterlitz-Thouless universal behaviour. The second transition is instead non-relativistic, with dynamical critical exponent $z > 1$. For the sake of comparison, we illustrate how some of the techniques applied here work at the Potts critical point present in the phase diagram of the model for finite next-nearest-neighbor repulsion. This latter application also allows to quantitatively estimate which system sizes are needed to match the conformal field theory spectra with experiments performing level spectroscopy., 18 pages, 14 figures

Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors. These order parameters quantitatively capture the entanglement that is possible to distill from the ground state manifold, and are thus quantized to 0 or log 2. Their robust quantization property is inferred from the underlying lattice gauge theory description of topological superconductors, and is corroborated via exact solutions and numerical simulations. Transitions between topologically trivial and non-trivial phases are accompanied by scaling behavior, a hallmark of genuine order parameters, captured by entanglement critical exponents. These order parameters are experimentally measurable utilizing state-of-the-art techniques., 6 pages, 8 figures. Supp Mat: 9 pages, 8 figures v2: Fused the two files into one, added a new section on disorder. Modifed the text and added relevant references. Now: 12 pages, 11 figures