Exotic Ising dynamics in a Bose-Hubbard model

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.