Type-II fractons from coupled spin chains and layers

Abstract

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.