  Non-Hermtian (NH) Hamiltonians effectively describing the physics of
dissipative systems have become an important tool with applications ranging
from classical meta-materials to quantum many-body systems. Exceptional points,
the NH counterpart of spectral degeneracies, are among the paramount phenomena
unique to the NH realm. While realizations of second-order exceptional points
have been reported in a variety of microscopic models, higher-order ones have
largely remained elusive in the many-body context, as they in general require
fine tuning in high-dimensional parameter spaces. Here, we propose a
microscopic model of correlated fermions in three spatial dimensions and
demonstrate the occurrence of interaction-induced fourth-order exceptional
points that are protected by chiral symmetry. We demonstrate their stability
against symmetry breaking perturbations and investigate their characteristic
analytical and topological properties.
