  Explorations of symmetry and topology have led to important breakthroughs in
quantum optics, but much richer behaviors arise from the non-Hermitian nature
of light-matter interactions. A high-reflectivity, non-Hermitian optical mirror
can be realized by a two-dimensional subwavelength array of neutral atoms near
the cooperative resonance associated with the collective dipole modes. Here we
show that exceptional points develop from a nondefective degeneracy by lowering
the crystal symmetry of a square atomic lattice, and dispersive bulk Fermi arcs
that originate from exceptional points are truncated by the light cone. We also
find, although the dipole-dipole interaction is reciprocal, the
geometry-dependent non-Hermitian skin effect emerges. Furthermore, skin modes
localized at a boundary show a scale-free behavior that stems from the
long-range interaction and whose mechanism goes beyond the framework of
non-Bloch band theory. Our work opens the door to the study of the interplay
among non-Hermiticity, topology, and long-range interaction.
