Finite-Temperature Quantum Topological Order in Three Dimensions

Explore a 34-minute conference talk by Curt von Keyserlingk presented at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) during the Thematic Programme on "Entanglement in Many-body Quantum Matter: Dynamics, Dissipation, Equilibration." Discover a groundbreaking identification of a three-dimensional system exhibiting long-range entanglement at small but nonzero temperatures, constituting quantum topological order at finite temperature. Learn about the fermionic toric code, a variant of the standard 3D toric code, which features emergent fermionic point-like excitations and possesses an anomalous 2-form symmetry associated with space-like Wilson loops. Understand how this symmetry creates a novel topological order and long-range entanglement in low-temperature thermal states. Examine the hypothesis that these states belong to an equilibrium phase of matter existing only at nonzero temperatures, and consider the conjecture that other examples of topological orders at nonzero temperatures may be found in discrete gauge theories with anomalous 2-form symmetries—opening new avenues for studying quantum topological order at nonzero temperature in physically realistic dimensions.