A Holographic Principle for Local Topological Order

Explore a fascinating lecture on local topological order and its connection to a holographic principle. Delve into the world of topological order in (2+1)D quantum many-body systems, characterized by anyonic quasi-particle excitations. Examine the recent interest in microscopic models exhibiting local topological order, focusing on local Hamiltonians of spin systems that are frustration-free and capable of error correction in finite regions. Discover how local degrees of freedom concentrate near region boundaries, suggesting a "local holographic principle." Learn how this concept is formalized using operator algebra language, and understand how the entanglement of bulk state spaces translates to algebraic entanglement of boundary algebras, ultimately allowing for the recovery of bulk topological order.