  In a recent experiment on CoNb_2O_6, Coldea et al. [Science 327, 177 (2010)]
found for the first time experimental evidence of the exceptional Lie algebra
E_8. The emergence of this symmetry was theoretically predicted long ago for
the transverse quantum Ising chain in the presence of a weak longitudinal
field. We consider an accurate microscopic model of CoNb_2O_6 incorporating
additional couplings and calculate numerically the dynamical structure function
using a recently developed matrix-product-state method. The excitation spectra
show bound states characteristic of the weakly broken E_8 symmetry. We compare
the observed bound state signatures in this model to those found in the
transverse Ising chain in a longitudinal field and to experimental data.
