  Non-Hermitian systems exhibit novel phenomena without Hermitian counterparts,
such as exceptional points and the non-Hermitian skin effect. These
non-Hermitian topological phenomena are observable in single-particle
excitations of correlated systems in equilibrium, which are described by
Green's functions. In this paper, we demonstrate the appearance of the hinge
non-Hermitian skin effect in the effective Hamiltonian that describes the
single-particle properties of an $f$-electron system. Skin effects result in a
strong sensitivity to boundary conditions, and a large number of eigenstates
localize at one boundary when open boundary conditions are applied. Our system
exhibits such sensitivity and hosts skin modes localized around hinges. This
hinge skin effect is induced by a non-Hermitian topology of the surface
Brillouin zone. The hinge skin modes are observed for one-dimensional
subsystems located between one pair of exceptional points in the surface
Brillouin zone. This paper highlights that correlated materials are an exciting
platform for analyzing non-Hermitian phenomena.
