Towards Non-Invertible Anomalies from Generalized Ising Models

Understand

We present a general approach to the bulk-boundary correspondence of noninvertible topological phases, including both topological and fracton orders.

• This is achieved by a novel bulk construction protocol where solvable $(d+1)$-dimensional bulk models with noninvertible topology are constructed from the so-called generalized Ising (GI) models in $d$ dimensions.
• The GI models can then terminate on the boundaries of the bulk models.
• The construction generates abundant examples, including not only prototype ones such as $Z_2$ toric code models in any dimensions no less than two, and the X-cube fracton model, but also more diverse ones such as the $Z_2\times Z_2$ topological order, the 4d $Z_2$ topological order with pure-loop excitations, etc.