Non-Hermitian Symmetric Nodal Phases
by
Albano 3: 5230 - Xenon (12 seats)
Albano Building 3
Using homotopy theory, we classify nodal structures of non-Hermitian systems under a range of symmetries. Without any additional symmetries, non-hermitian degenerate operators are related to a braid group-valued topological invariant. This invariant is non-Abelian, which forbids a naïve extension of the fermion-doubling theorem to non-hermitian systems. In art.[1] we show that this can lead to non-Abelian monopole charges. In art.[2] we consider spatial symmetries of crystalline systems in two dimensions, and show that these can enforce degenerate points. Additional anti-unitary symmetries can enforce exceptional lines, a uniquely non-Hermitian phenomenon. In art.[3] we investigate the homotopy structure of 𝓟𝓣-symmetric operators in general, and use it to classify non-Hermitian degeneracies for these systems.
