  We establish the appearance of a qualitatively new type of spin liquid with
emergent exceptional points when coupling to the environment. We consider an
open system of the Kitaev honeycomb model generically coupled to an external
environment. In extended parameter regimes, the Dirac points of the emergent
Majorana fermions from the original model are split into exceptional points
with Fermi arcs connecting them. In glaring contrast to the original gapless
phase of the honeycomb model which requires time-reversal symmetry, this new
phase is stable against all perturbations. The system also displays a large
sensitivity to boundary conditions resulting from the non-Hermitian skin effect
with telltale experimental consequences. Our results point to the emergence of
new classes of spin liquids in open systems which might be generically realized
due to unavoidable couplings with the environment.
