Dynamics of quantum spin chains from integrability

The study of several quantum magnetic phenomena in this thesis is driven by the experimental realizability of quantum spin chain models of one-dimensional magnetism. The theoretical models employed to study these physical phenomena are integrable quantum spin chains, in particular the anisotropic Heisenberg spin-1/2 model and the Babujan-Takhtajan spin-1 model, while additional (non-)integrable magnetic potentials or spin-spin interactions are considered as well.
The dynamics of spin chains are computationally accessible by numerically summing up large amounts of matrix elements of local spin operators between eigenstates of the quantum integrable spin models in a parallelized fashion. The availability of matrix element expressions from quantum integrability constitutes an important connection between the deep mathematical structure of integrable spin chains and experimentally measurable local observables and correlations on magnetic systems.
By the aforementioned integrability based method, the dynamics of quasi-particles of quantum spin chains can be assessed. In particular, the scattering effects of bound magnons, the time evolution of spinons, and time-evolution with additional integrability-breaking spin-spin interactions are computed and visualized. Moreover, for several cases the dynamical structure factor is computed, which is relevant to inelastic neutron scattering experiments. Extensions to correlations away from the ground state are investigated, providing opportunities of studying thermal correlations as well.