Topological invariants for symmetry-protected topological phase entanglers
Carolyn Zhang
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.
Topics & Concepts
Unitary stateSymmetry (geometry)Topology (electrical circuits)Operator (biology)Symmetry protected topological orderPhysicsUnitary operatorLocalityTopological entropy in physicsTopological orderTheoretical physicsQuantumMathematicsTopological quantum numberQuantum mechanicsGeometryCombinatoricsHilbert spacePhilosophyBiochemistryChemistryTranscription factorLawRepressorGeneLinguisticsPolitical scienceQuantum many-body systemsTopological Materials and PhenomenaQuantum and electron transport phenomena