Professor David Penneys
OSU Department of Mathematics
Local Topological Order and Boundary Algebra
Location: 1080 Physics Research Building
Faculty Host: Yuan-Ming Lu
Abstract: Bravyi, Hastings, and Michalakis introduced certain topological quantum order (TQO) axioms to ensure gap stability of a commuting projector local Hamiltonian and stabilize the ground state space with respect to local operators in a quantum spin system. In joint work with Corey Jones, Pieter Naaijkens, and Daniel Wallick (arXiv:2307.12552), we introduce a set of local topological order (LTO) axioms which imply the TQO conditions of Bravyi-Hastings-Michalakis, and we show our LTO axioms are satisfied by known 2D examples, including Kitaev's toric code and Levin-Wen string net models associated to unitary fusion categories (UFCs). From the LTO axioms, we can produce a canonical net of algebras on a codimension 1 sublattice which we call the net of boundary algebras. The boundary nets for these examples are isomorphic to fusion categorical nets arising directly from the UFC. For these UFC nets, Corey Jones' category of DHR bimodules recovers the Drinfeld center, leading to a bulk-boundary correspondence where the bulk topological order is described by 'local' representations of the boundary net.
