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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 ofemitter excitation is proportional to the inverse of the distance and equalsthe lattice dimension. For two species of emitters in an alternatingarrangement, the single excitation sector exhibits non-Hermitian spectralsingularities known as exceptional points. We unveil an unconventional phasetransition, dubbed exceptional-point phase transition, from the collective toindividual spontaneous emission behaviors. At the transition point, the $N\times N$ Hamiltonian fragments into $N/2-1$ many two-dimensionalnon-diagonalizable blocks. The remaining diagonalizable block contains adissipation-induced edge state with algebraically localized profiles, and weprovide numerical evidence for its existence in the infinite-array limit. Wedemonstrate that the edge state can be eliminated via a continuous deformation,consistent with the ill-definedness of bulk topological invariant. We alsopropose a spatially resolved character to quantify the incoherent flow and lossin the non-unitary quantum walks of single atomic excitations.

Alternating quantum-emitter chains: Exceptional-point phase transition, edge state, and quantum walks