Entanglement in spin chains

The recent interest in aspects common to Quantum Information Theory and Condensed Matter Physics has prompted prosperous activity at the border of these two disciplines, which were far distant only a few years ago. Numerous interesting questions have been addressed so far. In particular the meaning of “quantum correlations” has been refined beyond the generic notion of “correlations in a quantum system”. The best-known example of “pure” quantum-mechanical correlation is entanglement, but other facets of quantumness have been recently evidenced in quantum systems.In this lecture I will summarize some of the properties of the entanglement and other quantum correlations in extended (many-body) systems. I will mostly consider interacting spins localized in a low-dimensional lattice where quantum-mechanical effects are the most pronounced. I will discuss how this perspective allows us to disclose new features of the physical behavior of the system, with potential spin-offs for the understanding of puzzling problems in Condensed Matter Physics. I will also address the problem of systems out of equilibrium, sketching how to generate and manipulate entangled states by means of many-body Hamiltonians.