Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes

TL;DR

This paper introduces recoverable information as a new measure for stabilizer Hamiltonians, revealing topological features and emergent conservation laws in fracton models, with multiple calculation methods and practical demonstrations.

Contribution

It defines recoverable information, proves its calculation equivalence, and applies it to fracton models to uncover emergent conservation laws and constraints.

Findings

Recoverable information quantifies topological data in stabilizer models.

Multiple methods for calculating recoverable information are shown to be equivalent.

Emergent $Z_2$ conservation laws are deduced from recoverable information in fracton models.

Abstract

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.