  When the quantum critical transverse-field Ising chain is perturbed by a
longitudinal field, a quantum integrable model emerges in the scaling limit
with massive excitations described by the exceptional $E_{8}$ Lie algebra.
Using the corresponding analytical form factors of the quantum $E_{8}$
integrable model, we systematically study the spin dynamic structure factor of
the perturbed quantum critical Ising chain, where particle channels with total
energy up to 5$m_1$ ($m_1$ being the mass of the lightest $E_{8}$ particle) are
exhausted. In addition to the significant single-particle contributions to the
dynamic spectrum, the two-particle channels with different masses are found to
exhibit an edge singularity at the threshold of the total mass and decay with
an inverse square root of energy, which is attributed to the singularity of the
two-particle density of states at the threshold. The singularity is absent for
particles with equal masses due to a cancellation mechanism involving the
structure of the form factors. As a consequence, the dynamic structure factor
displays a cascade of bumping peaks in the continuum region with clear singular
features which can serve as a solid guidance for the material realization of
the quantum $E_{8}$ model.
