This volume presents a collection of review papers on recent work in the connected areas of strongly correlated systems, the effects of coherence on macroscopic systems, and entanglement in quantum systems. These areas have attracted considerable interest due to their complexity and associated unexpected nontrivial phenomena, and also due to their potential applications in various fields, from materials science to information technology. The coverage includes strongly correlated electronic systems such as low-dimensional complex materials, ordered and disordered spin systems, and aspects of the physics of manganites and graphene, both in equilibrium and far from equilibrium.

This book is a collection of articles on the contemporary status of quantum mechanics, dedicated to the fundamental issues of entanglement, decoherence, irreversibility, information processing, and control of quantum evolution, with a view of possible applications. It has multidisciplinary character and is addressed at a broad readership in physics, computer science, chemistry, and electrical engineering. It is written by the world-leading experts in pertinent fields such as quantum computing, atomic, molecular and optical physics, condensed matter physics, and statistical physics.

During the past two decades, thanks to the mutual fertilization of the research in quantum information and condensed matter, new approaches based on purely quantum features without any classical analog turned out to be very useful in the characterization of many-body quantum systems (MBQS). A peculiar role is obviously played by the study of purely quantum correlations, manifesting in the "spooky" properties of entanglement and nonlocality (or Bell correlations), which ultimately discriminate classical from quantum regimes. It is, in fact, such kind of correlations that give rise to the plethora of intriguing emergent behaviors of MBQS, which cannot be reduced to a mere sum of the behaviors of individual components, the most important example being the quantum phase transitions. However, despite being indeed closely related concepts, entanglement and nonlocality are actually two different resources.With regard to the entanglement, we will use it to characterize several instances of MBQS, to exactly locate and characterize quantum phase transitions in spin-lattices and interacting fermionic systems, to classify different gapped quantum phases according to their topological features and to provide a purely quantum signature of chaos in dynamical systems.Our approach will be mainly numerical and for simulating the ground states of several one-dimensional lattice systems we draw heavily on the celebrated "density matrix renormalization group" (DMRG) algorithm in the "matrix product state" (MPS) ansatz. A MPS is a one-dimensional tensor network (TN) representation for quantum states and occupies a pivotal position in what we have gained in thinking MBQS from an entanglement perspective. In fact, the success of TNs states mainly relies on their fulfillment, by construction, of the so called "entanglement area law". This is a feature shared by the ground states of gapped Hamiltonians with short-range interactions among the components and consists of a sub-extensive entanglement entropy, which grows only with the surface of the bipartition. This property translates in a reduced complexity of such systems, allowing affordable simulations, with an exponential reduction of computational costs. Besides the use of already existing TN-based algorithms, an effort will be done to develop a new one suitable for high-dimensional lattices.While many useful results are available for the entanglement in many different contexts, less is known about the role of nonlocality. Formally, a state of a multi-party system is defined nonlocal if its correlations violate some "Bell inequality" (BI). The derivation of the BIs for systems consisting of many parties is a formidable task and only recently, a class of them, relevant for nontrivial states, has been proposed. In an important chapter of the thesis, we apply these BIs to fully characterize the phase transition of a long-range ferromagnetic Ising model, doing a comparison with entanglement-based results and then making one of the first efforts in the study of MBQS from a nonlocality perspective.

This book summarizes the basic physics of graphite and newly discovered phenomena in this material. The book contains the knowledge needed to understand novel properties of functionalized graphite demonstrating the occurrence of remarkable phenomena in disordered graphite and graphite-based heterostructures. It also discusses applications of thin graphitic samples in future electronics. Graphite consists of a stack of nearly decoupled two-dimensional graphene planes. Because of the low dimensionality and the presence of Dirac fermions, much of graphite physics resembles that of graphene. On the other hand, the multi-layered nature of the graphite structure together with structural and/or chemical disorder are responsible for phenomena that are not observed yet in graphene, such as ferromagnetic order and superconductivity. Each chapter was written by one or more experts in the field whose contributions were relevant in the (re)discovery of (un)known phenomena in graphite. The book is intended as reference for beginners and experts in the field, introducing them to many aspects of the new physics of graphite, with a fresh overview of recently found phenomena and the theoretical frames to understand them.

The chapters included in the book describe recent developments in the field of superconductivity. The book deals with both the experiment and the theory. Superconducting and normal-state properties are studied by various methods. The authors presented investigations of traditional and new materials. In particular, studies of oxides, pnictides, chalcogenides and intermetallic compounds are included. The superconducting order parameter symmetry is discussed and consequences of its actual non-conventional symmetry are studied. Impurity and tunneling effects (both quasiparticle and Josephson ones) are among topics covered in the chapters. Special attention is paid to the competition between superconductivity and other instabilities, which lead to the Fermi surface gapping.