  We study the long-range hopping limit of a one-dimensional array of $N$
equal-distanced quantum emitters in free space, where the hopping amplitude of
emitter excitation is proportional to the inverse of the distance and equals
the lattice dimension. For two species of emitters in an alternating
arrangement, the single excitation sector exhibits non-Hermitian spectral
singularities known as exceptional points. We unveil an unconventional phase
transition, dubbed exceptional-point phase transition, from the collective to
individual spontaneous emission behaviors. At the transition point, the $N
\times N$ Hamiltonian fragments into $N/2-1$ many two-dimensional
non-diagonalizable blocks. The remaining diagonalizable block contains a
dissipation-induced edge state with algebraically localized profiles, and we
provide numerical evidence for its existence in the infinite-array limit. We
demonstrate that the edge state can be eliminated via a continuous deformation,
consistent with the ill-definedness of bulk topological invariant. We also
propose a spatially resolved character to quantify the incoherent flow and loss
in the non-unitary quantum walks of single atomic excitations.
