  Correlated materials have appeared as an arena to study non-Hermitian effects
as typically exemplified by the emergence of exceptional points. We show here
that topological Kondo insulators are an ideal platform for studying these
phenomena due to strong correlations and surface states exhibiting a nontrivial
spin texture. Using numerical simulations, we demonstrate the emergence of
exceptional points in the single-particle Green's function on the surface of
the material while the bulk is still insulating. We reveal how quasiparticle
states with long lifetimes are created on the surface by non-Hermitian effects
while the Dirac cones are smeared, which explains the surface Kondo breakdown
at which heavy Dirac cones disappear from the single-particle spectrum and are
replaced by light states. We further show how the non-Hermiticty changes the
spin texture inherent in the surface states, which might help identify
exceptional points experimentally. Besides confirming the existence of
non-Hermitian effects on the surface of a topological Kondo insulator, this
paper demonstrates how the eigenstates and eigenvalues of the effective
non-Hermitian matrix describing the single-particle Green's function help
understand the properties of correlated materials.
