Bound states and E₈ symmetry effects in perturbed quantum Ising chains

In a recent experiment on CoNb₂O₆, R. Coldea [ScienceSCIEAS0036-807510.1126/science.1180085 327, 177 (2010)] found experimental evidence of the exceptional Lie algebra E₈. 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 CoNb₂O₆ 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.