Homotopy characterization of non-Hermitian Hamiltonians
Charles C. Wojcik, Xiao-Qi Sun, Tomáš Bzdušek, Shanhui Fan
Abstract
There has been much recent interest in understanding topological band theory of non-Hermitian systems. Most work has focused on the Chern number in these systems, although interesting phenomena related to an eigenvalue winding number has also been reported. Here, the authors give a complete topological classification using homotopy theory. They find that the Chern number can be reduced modulo 2 depending on the winding number, and this is interpreted in terms of braiding of Weyl points and exceptional nodal rings.
Topics & Concepts
HomotopyHermitian matrixMathematicsCharacterization (materials science)ModuloWinding numberEigenvalues and eigenvectorsChern classPure mathematicsManifold (fluid mechanics)Topology (electrical circuits)Algebra over a fieldPhysicsDiscrete mathematicsMathematical analysisCombinatoricsQuantum mechanicsMechanical engineeringOpticsEngineeringQuantum Mechanics and Non-Hermitian PhysicsTopological Materials and PhenomenaQuantum chaos and dynamical systems