Para-Hermitian perturbation theory and nodal lines in magnon systems

Para-Hermitian Hamiltonians are commonplace in many areas of physics, arising from Bogoliubov Hamiltonians of bosons. These are achieved, for example, in magnon and triplon systems as well as in interacting condensates. We present a systematic quasidegenerate perturbation theory scheme for para-Hermitian Hamiltonians, which faithfully reproduces the spectrum of any set of neighbouring energy eigenstates order by order, regardless of possible degeneracies. As an application, we show how the constraint of magnetic inversion symmetry (i.e. PT symmetry) generically gives rise to nodal lines in magnon band structures, much like in spinless electron systems. We verify our predictions by studying a spin model for CoTiO3, in which topological magnonic nodal lines have recently been discovered.