Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes

We introduce a new quantity, that we term recoverable information, defined for stabilizer Hamiltonians. For such models, the recoverable information provides a measure of the topological information, as well as a physical interpretation, which is complementary to topological entanglement entropy. We discuss three different ways to calculate the recoverable information, and prove their equivalence. To demonstrate its utility, we compute recoverable information for fracton models using all three methods where appropriate. From the recoverable information, we deduce the existence of emergent $Z_2$ Gauss-law type constraints, which in turn imply emergent $Z_2$ conservation laws for point-like quasiparticle excitations of an underlying topologically ordered phase.