Classification of symmetry protected topological phases in quantum spin chains
Yoshiko Ogata
Abstract
We consider the classification problem of symmetry protected topological (SPT) phases on quantum spin systems.SPT phases are gapped short-range-entangled quantum phases with a symmetry G.We explain that in one and two-dimensional quantum spin systems, there are H 2 (G, U (1))/ H 3 (G, U (1))-valued invariant, confirming a physicists conjecture. Contents1. Symmetry protected topological phases 41 2. SPT-phases in 1-dimensional systems 63 3. SPT-phases in 2-dimensional systems 78
Topics & Concepts
PhysicsSymmetry (geometry)Quantum phasesQuantumSpin (aerodynamics)Invariant (physics)Symmetry protected topological orderTopological orderTheoretical physicsConjectureTopology (electrical circuits)Quantum mechanicsQuantum phase transitionMathematicsGeometryCombinatoricsThermodynamicsQuantum many-body systemsPhysics of Superconductivity and MagnetismQuantum and electron transport phenomena