RESUMEN
Linear spin wave theory (LSWT) is the standard technique to compute the spectra of magnetic excitations in quantum materials. In this Letter, we show that LSWT, even under ordinary circumstances, may fail to implement the symmetries of the underlying ordered magnetic Hamiltonian leading to spurious degeneracies. In common with pseudo-Goldstone modes in cases of quantum order by disorder these degeneracies tend to be lifted by magnon-magnon interactions. We show how, instead, the correct symmetries may be restored at the level of LSWT. In the process we give examples, supported by nonperturbative matrix product based time evolution calculations, where symmetry dictates topological features but where LSWT fails to implement them. We also comment on possible spin split magnons in MnF_{2} and similar rutiles by analogy to recently proposed altermagnets.
RESUMEN
We introduce a matrix-product state based method to efficiently obtain dynamical response functions for two-dimensional microscopic Hamiltonians. We apply this method to different phases of the Kitaev-Heisenberg model and identify characteristic dynamical features. In the ordered phases proximate to the spin liquid, we find significant broad high-energy features beyond spin-wave theory, which resemble those of the Kitaev model. This establishes the concept of a proximate spin liquid, which was recently invoked in the context of inelastic neutron scattering experiments on α-RuCl_{3}. Our results provide an example of a natural path for proximate spin liquid features to arise at high energies above a conventionally ordered state, as the diffuse remnants of spin-wave bands intersect to yield a broad peak at the Brillouin zone center.