We study the effect of disorder on $Z_2$ 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 $\mathrm{Re}\left(E\right)=0$ states filling the area in between. We demonstrate the different scenarios using both toy models as well as large-scale numerical simulations.

• Received 6 February 2024
• Revised 28 March 2024
• Accepted 2 April 2024

DOI:https://doi.org/10.1103/PhysRevB.109.155162