Gauging a diagonal 1-form symmetry of stacked 2+1D topological orders implements p-string condensation, yielding 3+1D fracton phases such as the X-Cube and string-membrane-net models.
Type-II fractons from coupled spin chains and layers
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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.
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String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
Gauging a diagonal 1-form symmetry of stacked 2+1D topological orders implements p-string condensation, yielding 3+1D fracton phases such as the X-Cube and string-membrane-net models.