Quantum Lattice Systems - Observables, Dynamics, Ground States, and GNS Representation

Explore the fundamental concepts of quantum lattice systems in this 56-minute conference talk from Harvard CMSA's Workshop on Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras. Delve into the mathematical framework of quantum lattice systems, examining observables and their algebraic structure, the dynamics governing these systems, and the characterization of ground states. Learn about the GNS (Gelfand-Naimark-Segal) representation and its role in quantum statistical mechanics, understand the concept of ground state gaps and their physical significance, and work through concrete examples that illustrate these theoretical concepts. Gain insights into how quantum lattice systems serve as a bridge between abstract operator algebra theory and physical applications in condensed matter physics and quantum field theory.