  We show that interactions in quantum spin liquids can result in non-Hermitian
phenomenology that differs qualitatively from mean-field expectations. We
demonstrate this in two prominent cases through the effects of phonons and
disorder on a Kitaev honeycomb model. Using analytic and numerical
calculations, we show the generic appearance of exceptional points and rings
depending on the symmetry of the system. Their existence is reflected in
dynamical observables including the dynamic structure function measured in
neutron scattering. The results point to new phenomenological features in
realizable spin liquids that must be incorporated into the analysis of
experimental data and also indicate that spin liquids could be generically
stable to wider classes of perturbations.
