  Waveguide quantum electrodynamics constitutes a modern paradigm for the
interaction of light and matter, in which strong coupling, bath structure, and
propagation delays can break the radiative conditions that quantum emitters
typically encounter in free space. These characteristics intertwine the
excitations of quantum emitters and guided radiation modes to form complex
multiphoton dynamics. So far, combining the collective decay of the emitters
with the non-Markovian effects induced by the modes has escaped a full solution
and the detailed physics behind these systems remains unknown. Here we analyze
such a collective non-Markovian decay in a minimal system of two excited
emitters coupled to a one-dimensional single-band waveguide. We develop an
exact solution for this system in terms of elementary functions that unveils
hidden symmetries and predicts new forms of spontaneous decay. The collective
non-Markovian dynamics, which are strongly dependent on the vacuum coupling and
the detuning from the center of the band, show exotic features that can be
characterized with a simple and readily available criterion. Our analytic
methods shed light on the complexity of collective light-matter interactions
and open up a pathway for understanding multiparticle open quantum systems.
