Topological invariants for symmetry-protected topological phase entanglers

Abstract

Broad classes of symmetry protected topological (SPT) phases can be prepared from a product state by locality preserving unitary operators that respect the symmetry as a whole, but cannot be written as symmetric finite depth quantum circuits. This work provides a framework for obtaining explicit topological invariants of such unitary operators, based on a special easily computable flux insertion operator. For unitary operators that are SPT entanglers, these invariants are related to the cocycle that labels the SPT phase.