Introduction to Quantum Many-body Systems and Quantum Information

The aim of this course is to provide the basics on the necessary tools to understand quantum many-body systems from a quantum information perspective. We reviewed the theory of quantum entanglement and its quantification, its application in the study of quantum phase transitions, and its implications for quantum matter through the tensor network representation of quantum states. As a practical application, we explained the basics of the Density Matrix Renormalization Group algorithm, the most successful numerical tool in the study of the low-energy properties of 1d quantum lattice systems.