Reflection Positivity and Invertible Phases of 2D Quantum Many-Body Systems

Explore reflection positivity in two-dimensional quantum many-body systems through this 51-minute conference talk from Harvard CMSA's Workshop on Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras. Delve into the fundamental question of whether reflection positivity, typically assumed in topological phase classification via continuous quantum field theories, emerges naturally from microscopic descriptions in general quantum many-body systems where this property doesn't inherently hold. Examine how every invertible phase of two-dimensional lattice systems admits a reflection-positive representative and understand why inverse phases are represented by complex conjugate states. Learn about a newly introduced index that distinguishes these phases and its conjectural relationship to the chiral central charge, providing insights into the bridge between microscopic quantum systems and their effective field-theoretic descriptions.