Quantum Phase Diagrams - Order Parameters, Topological Invariants, Examples

Explore quantum phase diagrams through the lens of ground states in quantum lattice systems in this comprehensive lecture by Bruno Nachtergaele from UC Davis, delivered as part of Harvard CMSA's Workshop on Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras. Delve into the fundamental concepts of order parameters and their role in characterizing different quantum phases of matter. Examine topological invariants as powerful tools for distinguishing between quantum phases that cannot be connected by continuous deformations. Learn through concrete examples how these theoretical frameworks apply to real quantum many-body systems. Gain insights into the mathematical structures underlying quantum phase transitions and the emergence of exotic phases of matter. Understand how homotopy theory and operator algebras provide rigorous foundations for studying topological phases in quantum field theory contexts.