國立清華大學 數學系

Abstract Quantum matters are electronic fluids in materials, behave non-trivially, forming superconducting and/or insulating phases. These quantum matters can be described mathematically as vector bundles with physical symmetry constraints. We will show applying the K-theory, a systematical classification of these quantum matters is given and many real materials are found. We will also discuss “anyonic quantum matters” where the underlying mathematical structure is category theory. These “anyonic quantum matters” are building blocks for topological quantum computing. Last, we will discuss the “quantum entanglement” in these quantum matters. We show the entanglement Renyi entropy and entanglement negativity have geometric meanings and can be computed from (non)orientable manifolds.