Spurious topological entanglement entropy and subsystem symmetries in compactified cubic code

Compactifying one direction of the cubic code results in a family of two dimensional topological orders, equivalent to stacks of toric code enriched by translation symmetry. Surprisingly, some of these models have unbroken rigid 1D subsystem symmetries that lead to spurious contributions to the topological entanglement entropy. These spurious contributions can appear in a bulk computation of the topological entanglement entropy from a linear combination of subregion entropies with cancelling boundary terms. We introduce an entropic quantity that measures the presence of such spurious contributions.