Disorder and non-Hermiticity in Kitaev spin liquids with a Majorana Fermi surface

We study the effect of disorder on Z₂ quantum spin liquids with a Majorana Fermi line (respectively a surface in three dimensions), and we show that depending on the symmetries that are preserved on average, qualitatively different scenarios will occur. In particular, we identify the relevant non-Hermitian symmetries for which disorder will effectively split the Fermi line into two exceptional lines, with Re(E)=0 states filling the area in between. We demonstrate the different scenarios using both toy models as well as large-scale numerical simulations.