Type-II fractons from coupled spin chains and layers

Understand

We describe a construction of topological orders from coupled lower dimensional symmetry-protected topological orders, which is closely related to gauging a subsystem symmetry.

• Our construction yields both conventional topological orders and exotic fracton topological orders of type-I and type-II.
• In particular, we find a coupled spin chain construction of Haah's cubic code, and a coupled layer construction of Yoshida's fractal spin liquids.