Spin dynamics of a perturbed quantum critical Ising chain

Near-critical system can exhibit exotic excitations. When the quantum critical transverse-field Ising chain is perturbed by a longitudinal field, a quantum integrable model emerges with massive excitations described by the exceptional E₈ Lie algebra. Using analytical form factors of the quantum E₈ 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 5m₁ (m₁ being the mass of the lightest E₈ particle) are exhausted. Besides significant single -particle channels’ contribution to the dynamic spectrum, different multi-particle channels also exhibit rich features in the continuum region with a cascade of bumping peaks, which can serve as a solid base for guiding the material realization of the E₈ model. Our results support the recent series of experimental realizations of the quantum E₈ model in the material BaCo₂V₂O₈, laying down a concrete material ground to study physics beyond integrability.