  Strong quantum fluctuations in magnetic systems can create disordered quantum
spin liquid phases of matter which are not predicted by classical physics. The
complexity of the exotic phenomena on display in spin liquids has led to a
great deal of theoretical and experimental interest. However, understanding the
fundamental nature of the excitations in these systems remains challenging. In
this work, we consider the Lifshitz quantum critical point in a two-dimensional
frustrated $XY$ antiferromagnet. At this point, quantum fluctuations destroy
long range order, leading to the formation of an algebraic Lifshitz spin
liquid. We demonstrate that the bosonic magnon excitations are long-lived and
well-defined in the Lifshitz spin liquid phase, though paradoxically, the
dynamic structure factor has a broad non-Lorentzian frequency distribution with
no single-particle weight. We resolve this apparent contradiction by showing
that the Lifshitz spin liquid suffers from an infrared catastrophe: An external
physical probe always excites an infinite number of arbitrarily low energy
quasiparticles, which leads to significant radiative broadening of the
spectrum.
