Squaring the fermion: The threefold way and the fate of zero modes
Qiao-Ru Xu, Vincent Paul Flynn, Abhijeet Alase, Emilio Cobanera, Lorenza Viola, Gerardo Ortíz
Abstract
In the spirit of Dirac's derivation of a fermionic theory by ``taking the square root'' of the bosonic Klein-Gordon equation, the authors present here a squaring procedure, mapping fermionic to bosonic theories, that helps establish a threefold-way topological classification of stable noninteracting bosonic matter. The ephemeral nature of boundary states and the topological triviality of noninteracting, zero-temperature bosonic phases are supported by three no-go theorems, although excitations of those same phases may display topologically nontrivial characteristics.
Topics & Concepts
BosonFermionHomogeneous spacePhysicsParity (physics)Theoretical physicsSymmetry (geometry)Lattice (music)Topology (electrical circuits)Hermitian matrixQuantumBoundary (topology)Quantum mechanicsMathematicsGeometryCombinatoricsMathematical analysisAcousticsTopological Materials and PhenomenaQuantum Mechanics and Non-Hermitian PhysicsMechanical and Optical Resonators