Quantum matter

We will briefly review introductory topics in solid state/condensed matter physics for those who have not had a first class on the subject, and introduce / review second quantization.  We will emphasize the role and consequences of symmetries, including time-reversal symmetry, and symmetry-based theorems.  We will see how insulators can appear from adding interactions to free electrons in metals and how spin-spin interactions emerge, and we will also introduce enough quantum chemistry to understand how to build models for materials. In order to illustrate how new phenomena emerge from many interacting particles, we will study several spin models where long-range quantum entanglement emerges, with its host of fractional particles.  We will introduce the theoretical tools to understand several experimental techniques, as well as a few modern numerical techniques.