Entanglement in quantum many-body systems
Strongly correlated quantum systems exhibit a variety of exciting phenomena, such as exactly quantized edge currents or topologically ordered phases with exotic excitations with unconventional statistics. They cannot be described by the conventional framework of symmetry breaking, but are characterized by the non-trivial nature of their global quantum correlations, this is, entanglement.
In this lecture, I will explain how we can understand the physics of these systems by looking at them from an entanglement perspective. In particular, I will explain what makes the entanglement in these systems special, and how this naturally leads to an entanglement-based description, termed Tensor Networks, which allow to explicitly understand the role played by entanglement in these systems. I will then discuss various applications of these framework, including in particular the characterization of topologically ordered phases in one and higher dimensions, the role played by the boundary and its relation to the so-called entanglement spectrum, as well as the application of Tensor Networks as numerical tools for the simulation of strongly correlated quantum systems, such as in the Density Matrix Renormalization Group (DMRG) method.