Non-Linear Spectroscopy of Quantum Spin Chains

The dynamical spin structure factor plays a central role in revealing the many-body dynamics of quantum magnets. It is directly related, via fluctuation-dissipation, to the linear susceptibility, encoding the response of the system to a weak perturbing field. However, though often incredibly powerful and insightful, these quantities do not always resolve all of the key physics at play. In particular, the concrete identification of fractionalized excitations remains an outstanding challenge. The recent introduction of THz two-dimensional coherent spectroscopy to the world of quantum magnetism has made it possible to push beyond the linear regime and access non-linear susceptibilities, encoding higher-order dynamical correlations. In this talk, I will present a brief overview of some of the relevant challenges and opportunities within this non-linear regime, and discuss its application in the setting of one-dimensional quantum spin chains, whose fractionalized spinon (or domain wall) excitations provide a useful test case to investigate how non-linear spectroscopy can provide new information not accessible within conventional linear response.