  We explore the dynamical properties of a one-dimensional Bose-Hubbard model,
where two bosonic species interact via Feshbach resonance. We focus on the
region in the phase diagram which is described by an effective, low-energy
ferromagnetic Ising model in both transverse and longitudinal fields. In this
regime, we numerically calculate the dynamical structure factor of the
Bose-Hubbard model using the time-evolving block decimation method. In the
ferromagnetic phase, we observe both the continuum of excitations and the bound
states in the presence of a longitudinal field. Near the Ising critical point,
we observe the celebrated E8 mass spectrum in the excited states. We also point
out possible measurements which could be used to detect these excitations in an
optical lattice experiment.
